What publication establishes
That a list exists and that somebody put it out. That is the complete content of the claim. Everything people usually take from a published list, that the addresses belong to the service named at the top, that they are current, that they lead to the same place as each other, is inference layered on top of that one thin fact.
The inference might be sound. If you know who published a list, have reason to trust them, and got the list from them directly rather than from somebody repeating it, the inference is reasonable. Every one of those conditions is about provenance, and none of them can be checked by looking at the strings.
What a set can be shown to be
Character analysis reaches further than people expect and stops abruptly. It can show that all twelve are well formed, which they are. It can show that they do not resemble each other, which they do not, with the longest shared opening across all 66 pairs being 1 character. It can show that the symbol distribution across 672 characters looks like independent random output, which it does.
Those findings are worth having because their opposites would be alarming. A set where several addresses shared five leading characters would suggest somebody had been grinding lookalikes. A set with a malformed entry would suggest carelessness or worse. Neither appears here.
But every one of those findings is consistent with a set that somebody made up entirely. Generating twelve valid, unrelated, well distributed onion addresses takes a few seconds and no skill. Passing every statistical check on this site is the default state of any set of addresses, honest or not.
Where that leaves a reader
With the same problem they started with, which is deciding whom to believe, and slightly better equipped to notice when somebody is dressing up a weak claim as a strong one.
The specific move to watch for is a page that performs a real check and then lets its credibility spill onto a claim the check does not cover. A site that correctly reports address lengths and then tells you which one is the official address has done arithmetic and then made something up, and the arithmetic is doing the work of making the invention sound careful.
This site tries not to do that, which is why the boundary is stated on every record page and in full on what this explorer cannot tell you. The twelve strings are computed over honestly. Where they came from is not something arithmetic can answer.
Questions
Does publishing addresses together prove they are related?
No. It proves somebody grouped them. Whether they lead to the same service depends on who holds the keys, and nothing visible in a string reveals that.
Can any site verify an onion address for me?
A site can verify that a string is well formed, which is arithmetic. Verifying that it belongs to a particular operator requires information from that operator, not from the string.