Uncle Billy, the Parks carry deal cost him no votes and benefitted only a very few people. IOW, innocuous and made him no enemies. The Brady Bunch has little audience, generally.
My understanding is that as both a state senator and as a US senator, he voted in favor of all gun control bills that came up for a vote.
And some internal emails from DOJ to or from BATFE did indeed mention the political capital which could be had from making it look like Evil Dealers and gun shows let Terrible Guns go to Mexico. That's been known for quite some time.
People focus too much on the apparent views of the Main Man, and don't look at the views of appointees such as Holder. Holder's anti-gun views had to be well-known to Obama before the appointment. Easy enough for Obama to be out front making happy noises, while Holder et al work behind the scene. Ancient political game.
You're from BATFE? Come right in! I use all your fine products!