One does not truly access the blockchan without running a full node. Any other scenario involves reliance on a third party.
Do you understand what a peer-to-peer network is?
whats wrong with having a dumb peer that can't validate blocks and can only push TX's.
dumb peer-to-peer network
What's wrong?
It can be cheated.
You do understand the security implications of relying on SPV do you?