I have looked at this question and I am pretty sure I was the initial down-voter. (There were other down-voters who came after me.) The reason for my downvote was that I think your answer, as it originally appeared, was incorrect and misleading to the questioner. The particular assertion that I had the most concerns with, and led to my down-vote, was this:
....you can always make a phenomenological claim that the usage of phones by their users follows whatever distribution it follows AND that this distribution can be described by some model that is IID distributed on whatever distribution it needs to be to describe your data.
That assertion is false, or at best misleading. Asserting an IID structure to data is equivalent to asserting exchangeability of the data series, which certainly does not hold for all possible types of data. Perhaps you can make a "phenomenological claim" of IID data (whatever that means), but it will be clearly false in many instances. Exchangeability of data can be assessed empirically by runs tests, etc. If the phone-use data is not exchangeable (e.g., obvious order patterns; fails runs tests by wide margin) then it is not appropriate to assert that it is from an IID model structure. Moreover, in the context of the OP's question, he was interested in knowing how to tell if his two separate populations have independent values. There are certainly cases where this is false (e.g., paired values). Thus, I take the view that your original answer was incorrect on this point.
Anyway, that is the reason for my down-vote. The fact that there were other down-votes that came after mine suggests that others also had similar concerns (or maybe different concerns). Since you have now changed your answer to remove the previous incorrect assertion, and to improve your answer generally, I have now removed my down-vote. Since your new answer is quite a reasonable response to the question (much improved) I have added an up-vote instead. I hope this explanation helps in understanding why you received down-votes on that answer. Thanks for taking the time to improve your answer and seek feedback on Meta. I'm glad you are at peace. ;)
In regard to your broader question, "Is a sole answer with a down-vote worse than no answer at all", I would say that there is nothing wrong with keeping an answer with net down-votes. The fact that there are net down-votes to an answer is already a caution to the OP that the answer is disputed by other users on the site. So I would not think that this is any worse than no answer at all. It at least allows the OP to see one person's opinion, and the fact that this opinion is unpopular. That is sometimes valuable information.