That's not proof of fullnode, only proof of hash power. You can mine without being a full node as long as you have a full copy of the blockchain.
http://en.wikipedia.org/wiki/Duck_testEvery running miner (not a pool-miner, but owner of full node in setgenerate=true mode) works for decentralisation and been paid fees for founding blocks.
Such miners *must* accept transactions from the network and *must* push found blocks back to a network (otherwize it is wasting energy)
The problem is that mining on general devices is economically unreasonable. But we can do nothing with it.
You must understand that nobody will pay you only for your computer switched on.
I placed here a link
http://en.wikipedia.org/wiki/Tragedy_of_the_commonsFees and block reward - is a "common resource".