In this question the idea I put forward as a possible etymology for "ta" garnered the response that it is a well known false etymology for the word. That got me to wondering - being strictly a dabbler in matters of language - how are things proven or disproven in a field as fluid as the study of the origins and history of words and terminology? What tools does a linguist have at their disposal to trace words back and how are they applied?
In the matter of the answer you reference, you seem to be conflating plausibility with proof. It is not. Etymologists use a variety of methods, among which are:
Philological research. Changes in the form and meaning of the word can be traced with the aid of older texts, if such are available.
Making use of dialectological data. The form or meaning of the word might show variations between dialects, which may yield clues about its earlier history.
The comparative method. By a systematic comparison of related languages, etymologists may often be able to detect which words derive from their common ancestor language and which were instead later borrowed from another language.
The study of semantic change. Etymologists must often make hypotheses about changes in the meaning of particular words. Such hypotheses are tested against the general knowledge of semantic shifts. For example, the assumption of a particular change of meaning may be substantiated by showing that the same type of change has occurred in other languages as well.
Lexicographer Grant Barrett says etymologies need evidence:
published evidence that shows the etymological path. Dated, continuous, in-context quotations from any written source
We often have written evidence that a word is borrowed. For instance it will be marked by italics with a comment "as the Vikings say" or whatever. If you had such evidence then your claim about "ta" would be a lot stronger.
As is true for many subjects, it's easy to propose a theory that sounds plausible. But "based on ten minutes of research, my intuitive hunch, and something that my brother-in-law says his neighbor once overheard somebody say he read in a spam e-mail, I think this might be true" is a long way from "this is a proven fact". Add to that the fact that there are lots of etymological stories that appear to just be made up, maybe originally as a joke or someone trying to sound knowledgeable. (Again, this is true for many subjects, not just etymology.)
For example, I've seen lots of stories about various obscenities originally being acronyms, e.g. -- excuse me if I offend anyone here -- "Store High In Transit" supposedly being a label placed on shipping containers. Amusing, I suppose, but I have yet to see a single citation to an old document spelling out the acronym, it's always just one web site linking to another with the same unsubstantiated claim. Maybe there's really some evidence, but I wouldn't be surprised to learn that it was just a story somebody made up to be funny and others heard it and thought it was supposed to be true.
The fact that an English word sounds similar to a word from another language, or sounds like a contraction of a longer English word, is interesting and a valid basis for a theory. But such a similarity doesn't prove that's actually how we got the word. It might just be a coincidence, and often is. As Robusto says, you need to find a chain of old writings where you can actually trace the history. If you can actually find a document where somebody wrote, "... or I think we should call it ..." and makes up a new word, and then other documents citing that person as the inventor of the word, that would be strong evidence. But just, "it sounds sorta kinda similar to me" isn't strong evidence.