First off, take those statistics with a grain of salt. They didn't say "50%-70% drop out" because their GPA is too bad and their classes are too hard. I'm sure many of those people "drop out" despite a <3.5 GPA because, hell, it's just not what they want to do.
Also, bioengineering

re-med will not give you a full (and thus not a real) engineering degree. So "good job prospects" ? I doubt it.
But really, what gets me is that you want to do it "because it is so prestigous at UCSD." Is that why you want to be a doctor too? It's so prestigous? Prestige by itself is a moronic reason to do anything.
My advice? Please switch to something you actually like.