"We'll give you 20 bucks if you tell us who you bought these for"

It is harder than that though. Monero has an issue in that everyone is only doing ringsize=3 transactions, providing little anonymity. If you buy from an exchange then turn around and sell it back, even with different amounts, you will be on a shortlist of suspects.

To do Monero properly you need to wait a while (at least hours, better days) while churning to other addresses, being sure to keep your ringsize and fees looking like everyone else's. Hopefully they will raise the ringsize minimum to 10 in the upcoming hardfork - that will go some way towards fixing the problem.

For now, I bet there will be cases of people happily bouncing to Monero via Shapeshift and getting busted.

This is the correct answer.

And just how are you going to do a dollar <-> bitcoin exchange without revealing any information about your identity?