Doesn't match my experience. I know of plenty of startups that received EU funding with relatively little hassle. It's not that hard. And if you are afraid of some mild levels of bureaucracy, you shouldn't be running a company. And it's not like the US doesn't have bureaucracy.
Both is true: a lot of money is lost to bureaucracy and startups get funding, although it's not that easy imho. And the amounts are laughable in my experience, that's the biggest problem. Yes, it's nice that I get a kickback on research costs or whatever, but the process takes weeks and the returns are dismal. YMMV tho