[tryitnow]

You answer your own question when you state:

"The upper & middle class is more likely..."

"More likely" is the key term here. How much more likely? If they are very, very, very likely, then you might be correct.

However, if they're only slightly likely, then the social safety would be useful in catching those who would otherwise fall through the cracks.

There's issues around the direction of causality too. Why are the upper and middle classes likely to produce innovators?

Because of their upbringing?

Could part of that beneficial upbringing be the implicit social safety net they enjoy from their parents?