An opinion of sentiment that is morally certain, is that which excludes all prudent fear of falsity; so that the contrary opinion is regarded as wholly improbable.
This is how I would suggest parsing this.
First, we have to understand that the key issue for cases of conscience is prudence. Prudence makes a double showing here. First it appears explicitly: what is morally certain excludes all prudent fear of falsity. But it also appears implicitly: that the contrary opinion is regarded as wholly improbable. (In fact, I think that this definition is deliberately redundant -- it is a parallelism, and both clauses are two ways of making the same point.)
In other words, we are not talking of probability in our usual sense here (it is not chance of being correct, although there are etymological and historical connections between the two senses); it's a technical term. And Liguori, actually in the very passage where he gives the above definition, gives a meaning to it:
Saint Alphonsus Liguori, or, Extracts, translated from the Moral theology of the above Romish saint By Alfonso Maria de' Liguori, Richard Paul Blakeney
(I am, by the way not comfortable getting Liguori from Blakeney; but Blakeney gives the Latin and one could in principle check that against Liguori's Latin. It's difficult to find translations of important passages of Liguori into English online, and I don't have the time to stumble through on my own. One makes do with what one has.) So here we get an idea of what probability is: a moral opinion is probable when there is "some intrinsic reason or extrinsic authority" to which a prudent person, although in doubt, might assent. (The 'extrinsic authority' here would be the authority of someone with a reputation for good judgment in difficult moral matters; and this weighing of authorities is what the casuists usually talked about in discussing probability. But, as Liguori says here, the reasons inherent to the case itself also may play a major role.)
Second, morally certain opinions occur on a spectrum of probable opinions about whether a given act would be wrong:
(a) tenuiter probabilis (slightly probable): based on some reason a prudent person would have to take into account, but not such a one as would cause a prudent person to assent to it.
(a) probabilis: based on some reason that would cause a prudent person to assent to it, although there might still be doubt.
(b) probabilior: based on some reason that would cause a prudent person to assent to it, but with some prudent fear of the contrary being true (i.e., the better of two probable opinions)
(c) probabilissima: based on some reason that would cause a prudent person to assent to it, such that the contrary is only tenuiter probabilis.
(d) moraliter certa: based on some reason that would cause a prudent person to assent to it, such that the contrary is not even tenuiter probabilis.
Tuta (safe) and tutior (safer) have to do with how much is at stake, morally. Liguori's ultimate conclusion in all this will be his aequiprobabilism: that it is morally certain that when one opinion is more probable than the other, we should follow the more probable, but when two opinions are both probable, neither definitely more than the other, then you may choose as you see fit. That is, if you have good reason to think one way definitely more prudent than the other, you should follow the more prudent way; but if both can be prudently followed, even if one is riskier, morally speaking, you may make your own judgment. It's part of Liguori's battle with tutiorism, the view that you should always follow the view that risks less morally; in his view it is wicked to try to circumvent prudence by imposing obligations solely with a view to avoid even approaching the possibility of sinning -- it is morally wrong to treat one thing as obligatory when something contrary to it is also prudent, even if riskier. For one thing, he thinks that this can often lead to the wrong course of action; for another, prudence is prudence. For another, the context for all of this is confession and spiritual direction; your confessor, however, is not your judge, and it is not his business to decide matters of genuine controversy. And all of this does require that there be genuine controversy, not in the sense that people disagree, but that people with a reputation for good and sober judgment in moral matters, giving reasons a prudent person might accept, disagree.
So 'morally certain' in Liguori's sense is not about likelihood of error; it is about what reasons can be brought for and against a moral position to see if it is consistent with good judgment. Thus I think people are conflating two different senses of 'moral certainty' in this passage. In one, something that is morally certain is 'certain enough to act on'; in another, Liguori's, it is more like 'definitely the only prudent option'.
In any case, all of this is unnecessary for the broader discussion of which it is a part; the Church has a test -- I will not say it is always simple to apply, but it is straightforward to state and doesn't require digging into confessors' manuals. Is torture morally permissible? Of course, if you can torture someone charitably and consistently with the love of the God to whose image they are made. If torturing them would impede or hinder that love for them and for God, then it is wrong. And if it is simply inconsistent with them, it is wicked. And there's very little room for doubt as to the results of such a test here -- I would say no room, except that, human beings what they are, there will be people who will take a word and stretch it to things to which it doesn't rationally apply. But that aside, it's pretty clear that torturing someone is not a way to love them.
ADDED LATER: It would be better for everyone if all those who have opinions that are at most tenuiter probabilis, and all those who have principles that are tutiorist, were to bow out. That would mean very few people left in the discussion, I am afraid. But, of course, nobody thinks the opinion to which they are inclined is tenuiter probabilis, and tutiorists always think that they are the last bastion of righteousness (and these days never think of themselves as tutiorist). It's a discussion guaranteed to be artificially sustained, regardless of anything, including the danger of scandal.