I'm here to post some facts, make your own conclusions.
John Elway's postseason career:
[a: Shanahan WR coach, b: Shanahan QB coach, c: Shanahan offensive coordinator; d: Shanahan head coach]
1983: 0-1
1984a: 0-1
1985c: none
1986c: 2-1 (L Super Bowl)
1987c: 2-1 (L Super Bowl)
1988: none
1989b: 2-1 (L Super Bowl)
1990b: none
1991c: 1-1
1992: none
1993: 0-1
1994: none
1995d: none
1996d: 0-1
1997d: 4-0 (W Super Bowl)
1998d: 3-0 (W Super Bowl)
Total record: 14-8
Seasons with Shanahan: 11
Seasons without Shanahan: 5
Record with Shanahan: 14-6
Record without Shanahan: 0-2
Seasons with Terrell Davis: 4
Seasons without Terrell Davis: 12
Record with Terrell Davis: 7-1
Record without Terrell Davis: 7-7
Mike Shanahan's postseason career without Elway:
1988: none (Raiders HC)
1989: none (Raiders HC for 4 games; then went to Broncos as QB coach)
1992: 1-1 (49ers OC)
1993: 1-1 (49ers OC)
1994: 3-0 (49ers OC)
1999: none
2000: 0-1
2001: none
2002: none
2003: 0-1
Total record (including Elway): 19-10
Seasons with Elway: 11
Seasons without Elway: 10
Record with Elway: 14-6
Record without Elway: 5-4
The point isn't that Shanahan's necessarily the greatest coach or even the best fit for the Broncos right now. The point is that Shanahan has won without Elway -- a Super Bowl, in fact -- but Elway hasn't won without Shanahan working with him. Just something to think about.
Your average person is always looking for a situation when there's two people to see "who is the real person behind the success." Clearly, there are interaction effects that are taking place here, and maybe, someday, these people will understand this.