The reason Heidegger is in permanent political trouble is because of the Rectorate and its many “Sieg Heil!” speeches. He’s not in hot water because of “the fact that [he] seems from the beginning to share themes and, occasionally, language with Nazi intellectuals.”
I can see the point, but I think this underestimates the extent of the 'hot water' in which Heidegger is found. There are two sense in whihc you could say that Heidegger is in trouble "because of the Rectorate":
(1) That it is only the Rectorate (and his later handling of his relation to the Rectorate) that provides material for those critical of Heidegger on this point;
(2) That the Rectorate accelerated the development of the controversy with regard to Heidegger because (a) it removed a great deal of ambiguity by establishing a clear link not just Nazism generally but to Hitler's Nazism directly; and (b) having established a clear link, it has forcefully raised the question of how extensive the links are due to the implausibility of the Rectorate Nazism simply springing out of nowhere.
When understood in the sense of (2) I think the claim that Heidegger is in trouble because of the Rectorate is quite right; I think there are reasons to think that it is false if understood in the sense of (1), not least because of expanding research into pre-Rectorate links to Nazi and Nazi-associated intellectual movements which have (very slowly) started to play a larger and larger role in the controversy. Without the Rectorate such links on their own could never be regarded as unambiguous: the controversy would be less heated, due to judgment calls about degrees of similarity and extent of influences. But sooner or later, for any German intellectual in this period, the question will be raised as to where their position is located relative to various Nazi and Nazi-related streams of thought, and where questions are raised research will be done, arguments framed, and controversies developed. Such research is necessarily slow; it requires extensive examination of these Nazi strands of thought, and, as anyone knows who has had to dip into it in order to inquire into some point or other, this is not something just anyone can do, since it requires a certain sort of stomach and capacity to endure. Even with the Rectorate establishing that Heidegger was at one point not just intellectually associated with Nazi thoughts but was a Nazi it has only developed very slowly. It is even possible that the question would not yet have been raised in that alternative reality in which Heidegger died in 1930. But pressure of research would itself guarantee that it had been raised, and mere ambiguity of evidence is enough for controversy.
So I do agree entirely that without the Rectorate what we'd have would be "a far cry from the current, permanent, grinding Heidegger political scandal", which has been massively intensified by the fact that Heidegger was, in fact, a Nazi explicitly advocating Hitlerist principles, by everyone's admission, and, as I noted before, I think the argument at "Object-Oriented Philosophy" is entirely right to this extent. But this only mitigates a problem that comes up for any German intellectual in the 1920s and 30s who was not unequivocally in some sort of opposition to the lines of thought we find in Nazi intellectual movement. There is something of a cloud, for instance, over völkisch thinkers who seem to have had nothing to do with National Socialism, and who, as far as can be determined, did nothing worse than inherit (as Nazi thinkers themselves did) a particular set of late Romantic problems and concepts. That's how hot this water is, how extensive the cloud: even mere intellectual proximity raises questions and controversies. It may well be that the question of Heidegger's politics might no longer be "How Nazi is Heidegger?" but simply, "How Nazi-like is Heidegger?" But the latter question is an serious enough to cause problems. The controversy of Heidegger's politics even now is, after all, not one of guilt; there's no real dispute over whether Heidegger was a Nazi, or supported Hitler, or associated both of those things with his philosophical work, since all three are explicit facts and suffice for any and all question of guilt. But guilt doesn't really tell us much of anything on its own; the grinding controversy is not about guilt but vitiation, how much of Heidegger is vitiated by the link. But questions of vitiation automatically arise for any German intellectual in the period who wasn't obviously in some kind of opposition; being a German intellectual in the period whose claims have thematic and occasional verbal similarities to those of Nazi intellectuals will raise them more insistently, however much ambiguity there might be to suggest charitable readings. And, again, there are strands of thought -- for instance, pre-Nazi intellectual movements that are probably not even actual ancestors to Nazi intellectual movements -- where some controversy has been raised over this question of how much they are vitiated by similarity of problems and themes.
So, again, I don't think there's any way of avoiding such a controversy in Heidegger's case (as there would be if we had reasonably clear evidence that Heidegger opposed the Nazis); it might be delayed, it might be weakened, but such controversies are automatic if there is nothing to prevent them -- and in Heidegger's case there is nothing to prevent them, and, indeed, as noted in the posts at "Object-Oriented Philosophy," some weak but definite testimonies that would tend to encourage them.
But (to put the point in terms more obviously related to the topic of 20th-c. HoP, which is my primary topic here) I freely admit that part of my insistence on this is due to the fact that I think academics have slowly been building, whether they have noticed or not, toward a rather massive inquiry into the Nazi intellectual milieu in all its ramified parts, one that has been pretty much inevitable given the seriousness of Nazism, and I don't think there are many German intellectuals of the time who will be spared severe scrutiny down to the niggling details. Arguments have already been raised across a very wide and very diverse array of intellectuals, some significant preliminary skirmishes have taken place with more obvious cases, and they are only likely to increase. The dispute over Heidegger, in other words, is not an isolated event, to be explained solely with reference to Heidegger's explicit convictions at some point of his life; it is merely a prominent part of a massive front of controversy and debate, one in which death in 1930 might have made him less prominent, but one which certainly would still have overtaken him sooner or later. And I think that it's pretty much inevitable that association with Nazism, whether by influence, or by support, or by similarity, will end up being a long-running set of questions and problems for the history of the philosophy of this period; indeed, a set that will eventually be raised for everyone not in sharp opposition; and, for all we can tell at the moment, the questions may well be raised for as long as people doing history of philosophy spend any time on the twentieth century.