A share has nothing to do with the block. It is just some useless value sent to you, to see "how fast you work".
Then you really have no idea how Proof-of-Work works. A share IS a block, in fact. It's a matter of whether it meets the network difficulty. You are credited regardless of this, since you provided the pool valid work. In case you tried to game the pool and sent it invalid work, it will be rejected and will be noted on the pool.
"You do not process shares when solo-mining, because you do not have to submit proof of your processing power."
They actually do the "share work". A share is just a fast and useless calculation, used to measure your speed, while you "solve the block". It has nothing to do with the block solution itself.
The reason you don't submit shares when solo mining, like in pools, is because pools send you a target of difficulty 1, and check to see if the shares is >= diff 1, but solo mining, Bitcoin sends you the network target which is as of this post 11.2m.
A share is NOT a fast and useless calculation.