There are two "sides" to the licensing of each song. They aren't the sides you think. They are 1. the side for the songwriting and 2. the side for the recording. Each side needs to be licensed in order to use an original recording, whereas only the songwriting side needs to be licensed in order to _create_ a cover. That said, to _license_ the cover itself one would still need to license both sides (for the original songwriting and the new recording, though for the new recording it is often easier if the publisher of the cover and the creator of the cover are one in the same, even if only in terms of ownership and not the actual individual musicians).
The need to separately license both sides grows out of the fact that there are two distinct pieces of copyrighted material and different sets of people with their legal hands on each part. With the propensity for guest artists these days, especially in certain genres of what their proponents call "music" *cough*hip-hop*cough*, you can imagine just how many people could be involved in any one side, let alone both.
Whether there is one side to negotiate or two, and whether for a cover or not, in any given case the overall process is the same and equally open to all sorts of craziness in terms of who wants how many dollars.
That aside for the moment, and to comment on the overall subject in general, it is worth noting that both sides have been more than happy to license their music to these games, and that you would be amazed at the amount of money it sometimes takes to get one into a game. The only reason the fees aren't even higher is because there is _competition_. What do I mean by this? Well, there are a great many songs out there, as we all know, so these copyright holders can only push negotiations so high before those in control of the budget for the game will dump the song and move onto something else on their list. Unless all of the artists form a cartel to control these license fees, this form of competition is what keeps the production of these games even remotely affordable.
In the meantime, both the copyright holders and those licensing the copyrights (the game companies) are completely free to negotiate for what they want and to walk away at any time. That the labels have been doing one thing (happily licensing their side) and saying another (complaining about the licensing fees they are receiving) should be no surprise to anyone here on /., that's for sure.