From Cambridge dictionary. The latter example doesn’t make sense to me

Judging by your title, you understand it perfectly

The writer doubts whether his response is factual.

That's a very poorly written entry. There's a comma missing. That seems like it was meant for "unequivocally" but got botched in the edit.

This is one of those words where its negation is the only one in common usage. "Unequivocally" is super common and means that there is no ambiguity. I don't think I've ever heard someone use the word "equivocally".

I would say it can be interpreted in different ways. It could mean, for example, that all the patients died, or that all recovered partially.

don't use this word at all. "unequivocally" has unequivocal meaning and relevance. "equivocally" is unlikely to communicate much to anyone.

Not sure if this will help but the the example given by saying none they could either mean the patients haven’t recovered at all or some of the patients have partially or fully recovered. 

The only way I see this word is *un*equivocally. It has a similar meaning to "definitely" or "without a doubt". So, if you saw a really good movie, you could say: "That was *unequivocally* the best movie I've ever seen."

As others have said: 1) No patients have fully recovered because they all died. 2) No patients have fully recovered because they are all still sick. 3) Some patients have only partially recovered, some not at all, some died etc. 4) Those that did fully recover are no longer patients so no "patients" fully recovered.

“Equivocally” is really not used, but for some reason, “unequivocally” is pretty commonplace. It’s an emphatic way of saying unambiguously, decisively, and definitely, [no two ways about it](https://dictionary.cambridge.org/us/dictionary/english/there-s-no-two-ways-about-it): unequivocally. Imagine asking a politician a straightforward yes/no question, and their answer begins, “Well, as you know, I was born in a humble middle-class family, in a neighborhood that was very diverse, and my parents were–,” blah blah blah. They talk all around the question, but they don’t really address the question. They equivocate. They dodge the question, pretending to give a satisfactory answer, but really leaving too much room for [mis]interpretation, on purpose. This is equivocation. It is grammatical to say that politicians “answer questions equivocally,” but it’s not a native-sounding way to say it, in my opinion. A good, clear, common, but vulgar way to say it is that politicians “bullshit.”

I’ve never used it except as part of unequivocally. I use equivocate. Equivocally is just useless as an adverb these days.

That's why between the 2 definitions there is an "or". It doesn't need to be both.

Patients may have recovered, but none fully.

'None' is ambiguous in that it could mean the illness has a permanent effect on all patients or just that they haven't had time to recover yet. But it's a bizarre sentence and use of the word.

This word was received equivocally by the commenters.

The second example (the one in question) doesn't have two opposing. It is using the definition "able to be understood in two (or more) different ways. The respondent has technically answered the question (how many patients have fully recovered) but left it so vague that he could be describing any number of situations. For example, all the patients have partially recovered, no one has recovered at all, some have partially recovered while others haven't, everyone died.

OED: adverb In an equivocal manner. 1. 1579–1660 † So as to have the name without the properties implied in the name; nominally. Cf. equivocal adj. A.1. Obsolete. 1579 By flesh and bloud æquiuocally, he vnderstandeth the sacrament of the flesh and bloud of Christe. W. Fulke, Heskins Parleament Repealed in D. Heskins Ouerthrowne 208 a1620 Which whosoeuer lacketh, he is not properly, but equiuocally, a man. M. Fotherby, Atheomastix (1622) i. xiv. §4. 152 1660 Words abstracted from their proper sense & signification, loose the nature of words, & are only equivocally so called. R. South, Interest Deposed 5 2. 1645– By equivocal generation. See equivocal adj. A.3. 1645 Reptiles, which are equivocally bred. G. Wither, Great Assises in Parnassus 32 1828 Those foul reptiles..of filth and stench equivocally born. T. B. Macaulay, Miscellaneous Writings (1860) 419 physiology 3.a. 1630– So as to admit of a twofold or manifold application. 1630 Vocation may be taken equivocally or univocally. R. Brathwait, English Gentleman 124 c1790 The same word may be applied to different things in three ways..equivocally, when they have no relation but a common name. T. Reid, Letter in Works vol. I. 75/2 3.b. 1660– So as to convey a double meaning, ambiguously. 1660 I forgive Grotius in this, not having defined anything less equivocally. R. Coke, Justice Vindicated ii. 39 a1720 She spoke equivocally. J. Sheffield, Works (1753) vol. II. 153 1817 They [sc. the instructions] were so equivocally worded. J. Mill, History of British India vol. II. v. v. 551