No the reason Philly had no running game is Reid is a pass-whacky coach who calls 60% passes a game and has throughout his time in Philly. The Pats came out in a short pass coverage defense, 5 linebackers, 2 downlinemen, that's a setup that will only stop the run with excellent play and is fully intended to stop the short pass. And Reid kept to the short pass and fully abandoned the run in the second half (6 runs, 1 of which was a McNabb scramble so it's only 5 runs called). When Belichick sent out that wierd 2-5 lineup on the first play of the game he sent a message to Reid, he told Reid he knew Philly wouldn't seriously attempt to run; then Reid called 6 passing plays in a row, which basically sent the message to Belichick: you're right.
And that's why Philly lost. No QB can win passing 60% of the time when the other team KNOWS that's what they're going to do. Philly called more play action passes (faking the run) than actual runs, how stupid is that, everybody on the other team knew they weren't going to run and they expected the Pats to bite on the FAKE (note, 8 play action passes in the second half resulted in 6 incompletions and a net gain of 8 yards)! Just plain a bad game plan by Reid, no variations from what they'd done before, completely predictable offense against a team that has a great gameplanner and two weeks to watch tape, no QB can succeed in that situation.
I agree with most of your take...it is RARE that an NFL, or college team, can win the BIG ONE, with only passing....once you get to the championship game, the defenses are capable of adjusting...HOWEVER, you must of heard the commentary during the game commenting on how the running backs for Philly rarely could get past the line of scrimmage...YET, even with passing 60% of the time, and no ground game success, Philly STILL could have won...BUT, McNabb made three REALLY bad decisions, and gave up interceptions...AND, as you must have also heard the commentators say, Philly REALLY screwed up with clock managment in the last 1.5 minutes...really dumb stuff.
I believe it is FAIR to say (although I was pulling for NE), that Philly would have won if McNabb had NOT thrown THREE unwise (should have held on to the ball) passes, and if they hadn't wasted so much valuable time on their last possession.
Of course one of the LBs is a downlineman...