I think if we are to trust the mentioned WP article (permanent link to current version) at least in its most general claims, the answer is there. The article itself is poorly sourced, though.
It seems that both bene and bonum versions coexist as widely accepted (27K and 23K results in Google, respectively).
The original is in Greek: τὸν τεθνηκóτα μὴ κακολογεῖν (as pointed by Vincenzo) attributed to Chilon of Sparta by ca. 600 BC and attested in the III century AD. Note that it is formulated in negative: don't criticize, revile, lit. speak bad/evil. Even if we don't trust the claim that this is the first appearance of the aphorism, it is a fact that it was written in Antiquity. You can see the original Greek source transcribed here.
Note that the Greek κακός means bad, may mean ugly, but NOT wrong or false. κακολογεῖν, in turn, means to criticize rather than to lie. This, IMO, settles the point. The burden of proof, then, lies upon those claiming the false sense.
The first attested translation to Latin (according to WP) uses bonum and dates from 1433. One can doubt the fact it was the first, but whether the sentence was written there 585 years ago is something one can verify.
Note that even the bene version, de mortuis nil nisi bene dicendum is ambiguous and doesn't rule out the speak good things interpretation.
No one asked, but I think it is good to distinguish. Many people (me included, I think) tend to unconsciously idealize the Classics and identify quotes with directives of what is right to do. That could lead some to reinterpret what was written so that the aphorism actually matches what they think is right. I think the so-to-say Hungarian interpretation could be an example of that.
Now, there is a subtle but substantive difference between avoiding/being less prone to tell uncomfortable truths about someone, and actively telling false good things about them. And I think that point is far from addressed by any of the sentences, or even both mainstream interpretations.