I'll give you an example which may help explain why Mueller was fired.
Before the 2002 draft, when he decided to pursue Charles Grant with the first round pick we got from you all in the Ricky trade, he convinced Benson he needed one more trip up to Georgia to meet with Charles. Benson approved the trip, no questions asked, and of course everything was paid for with team money. Turns out Mueller attended Masters events in Augusta---on Benson's dime---without informing Benson.
That's one example...he did that sort of thing often. Another was his purchase---again with team money and without permission---of security monitors, which he placed in the coaches' meeting rooms, and which he used to "spy" on them. (I'm being entirely serious.)
Yet another incident was his insistence upon interviewing with our most hated rival, the Atlanta Falcons, multiple times. Benson gave permission, but Mueller continued to work with the Falcons beyond what Benson understood as their agreement.
When you add events like this to the simple fact that, after 2000, Randy Mueller's major free agency aquisitions were simply horrendous---then his firing is no mystery.
Want to know what those signings were?
2001
WR Albert Connell - Given a big contract to complement Joe Horn, he was beat out by journeyman Willie Jackson at receiver and was a major locker room problem, just as Mueller's NFL contacts had warned (warnings he brushed aside). He stole money from Deuce McAllister, and was a major factor in the team's utter collapse at the end of the season.
Other moves included trading 2000 fifth round pick Chad Morton, who led all rookie return men that year and caught 30 passes, for a sixth round pick who did not make the team, and a cornerback named Earthwind Moreland who also was cut after camp and dind't even merit a practice squad spot. Mueller replaced Morton with an undrafted free agent named James Fenderson, who is now out of the NFL.
2002
Before his firing, Mueller signed the following...
CB Dale Carter - Between injuries and suspensions, he hardly touched the field. Was nailed for gambling in the locker room with younger players.
TE David Sloan - Built up by Mueller to be the answers to all our tight end woes, Sloan dropped as many passes as he caught during his Saints tenure, got hurt, and was gone a year later.
RT Victor Riley - He spent the entire 2002 season on the bench, fat and lazy. He played a bit in 2003, and started throughout 2004, where he was a horrible liability on our offensive line, unable to pass block. It was not unusual to see Aaron Brooks roll immediately to his left after the snap to buy some more time, as he knew Riley's man would usually be coming very, very quickly. Beyond his pass blocking woes, Riley led the team in pre-snap penalties, and remained out of shape. We drafted right tackle Jammal Brown in the first round this year to replace him.
DT Grady Jackson - He started for much of 2002, played well through the first half of the season, and then was invisible. He was cut halfway through the 2003 season after missing many meetings and remaining so out of shape he couldn't play more than a couple dozen snaps a game.
Other assorted moves included trading all-pro, future Hall of Fame tackle Willie Roaf to the Chiefs for a second-day pick. In KC, Roaf has continued his HOF ways.
Mueller made some good moves---mainly in 2000, with the signing of Joe Horn and the trade for Aaron Brooks---and had a few decent draft picks, such as Darren Howard, LeCharles Bentley and Charles Grant. But his negatives FAR outweigh his positives, and unless he has undergone some sort of brain transplant, his domineering, micromanaging personality will conflict with Saban, who is a Type A micromanager himself.