If you see an answer with a net score of zero, it means one of three things:
- Not enough people saw the answer to read it, let alone vote.
- People read it, but thought, "Meh, this isn't bad, but it isn't good enough to warrant an upvote." Alternatively, they might have thought, "Meh, this isn't good, but it isn't bad enough for me to downvote."
- There were an equal number of upvotes and downvotes on the answer (you can see the number of upvotes and the number of downvotes at 1,000 reputation).
The first possibility, I'd guess, happens quite a lot. The answerer may have been "late to the party", so to speak, and answered long after the question was asked, or the answer was simply overshadowed by other answers that accumulated a lot of votes.
The second possibility simply means that the answer wasn't good or bad. (Yes, people are generally more willing to upvote than dowvote, which is why I included a caveat: some people won't want to give up one rep point.)
The third possibility means that the answer was controversial; this does happen, and means that people have quite strong views on it. If you check the vote count (once you reach 1,000 rep) and see that the voting's split, be wary, and read the comments under the answer to try to understand the disagreement.
Using that as a segue, you really should judge for yourself the answer, if possible; always read the comments below it, and the answer itself in its entirety. You shouldn't decide to "trust" or "distrust" an answer based solely on how other people have voted. Votes don't always correlate with quality; some of my best answers (in my opinion) have gotten very few or no votes, while some of my less good answers have gotten inordinate amounts of upvotes. This is often due to a question getting onto the Hot Network Questions list, as knzhou pointed out.
The takeaway? Judge for yourself. See if you can follow the logic of the answer, and ask questions of the answerer in a comment if you don't fully understand it.
But the main point is, can I trust zero vote answers?
Treat/trust them no differently from one-vote, minus-one-vote, or X-vote answers: Judge them based on how well you can follow them. Don't choose to blindly trust them if you don't understand them; always investigate for yourself.