I think you might be mistaking people saying Bulger was a good NFL QB for saying he was better than or a better option than a healthy Warner. He of course wasn't. But also, at that time (2003) Warner was simply physically unable to play. He
needed to be on the bench for 2003, (most of) 2004 and 2005. His hand and body finally rebounded for that 2nd chapter of his great career and he became a winning, elite QB again.
By the way the 2002 team lost their first 5 games, not 6 (you're thinking of 2000 when Warner hurt his hand at KC). Warner was hurt in the 4th game vs DAL, Jamie Martin started week 5 (another loss), then Bulger was put in in game 6.