Unless the discoverer of a block can explicitly state "I don't want to confirm a transaction unless it pays me > xx BTC in fees" then all transactions will get confirmed at the same rate. Is that the case?
That is exactly the case. The pool/miner decides what is included in the block. Currently most miners include all transactions in the block regardless of fee however that is slowly changing. Eligus pool I believe only includes transactions that include a fee in blocks they mine.
Also blocks have a finite fixed size. If there are more transactions than the size of the block then all miners must choose which transactions to include. Obviously they aren't going to drop any "paying" transactions.
Thus the average length of time it takes to confirm you transaction depends on how much of the network is including you in the next block. If 100% includes you then it will be ~10 minutes. If 50% includes you then it will be 20 minutes. If 1% includes you then it will be 16 hours.
Today w/ no fee ~100% of network includes you in next block.
Today w/ a fee ~100% of network includes you in next block.
However that may not be true in the future. Hashing takes resources and the block reward will continually decline (and eventually become 0). Mining pools will start to make decisions about how small of a transaction fee they will accept and that will start to differentiate how long various transactions take to confirm.
"Miners" can't force a fee they can simply choose to include a transaction or not include it. Future version of bitcoin client could even aproximate how long confirmations will take depending on the fee chosen.