The deal does seem to have changed this year with the BBC getting two games and BT four games in the third round, rather than three each.
There was only one occasion where the Beeb got three games in the third round, last season. Before that it was always two - and BT had three. There's certainly been a change but there would clearly have to be because, as mentioned, there are now no replays after the fourth round so the broadcasters have to show more matches in earlier rounds, hence why BT now have four in the third round and there's now a sixth pick.
There also used to be the chance for broadcasters to get extra games the following season if there was only one, or no, replay in any given round so they couldn't show one.
The whole contract is a bit mysterious, but one thing is absolutely for certain and that's the Beeb always have first pick in every round.