It's also a definite "yes" but it depends on who that member has gotten all the red trust from.  If it's from DT members, there might be a problem.  If it's from members not on DT, especially newbies with their own red trust, it's probably safe to say that the member can be trusted--but you always have to look at the reference link on the person's trust page where the negative is.  A lot of times if some idiot leaves retaliatory or otherwise just malicious feedback there won't be a link to anything to show that the receiver of the neg can't be trusted.

OP, take a look at my trust history and you'll see that there are probably more negatives than positives.  Does that mean you can't trust me?  No (though I'm sure there are some members who'd tell you otherwise).  Most of the red trust I've gotten has been from members I'd previously tagged for various misdeeds like account selling or abusing bounties.  The same is true for many members on the default trust list, because a lot of them are or have been active scam busters and have thus gotten a lot of negative trust in return from members they've busted. 

That's just how the trust system works.  Anyone can give anyone else a positive, neutral, or negative trust for any reason.  It's not like eBay's feedback system, where there has to be a verified transaction between people exchanging feedback.  In fact, TECSHARE was pushing for something like that before he died if I'm not mistaken.  I tend to think it would be an improvement on the current system, though there needs to be a way for members to warn others of scammers before scams occur--and that's where the current trust system has its value.