You're acting like Shanahan was purely a ground and pound guy back then. Fact of the matter is the Broncos ranked 7th, 9th, 13th and 7th in passing from 1995 to 1998 while Shanahan was the coordinator and Elway was the quarterback. Hell, the Redskins even this year with that Grossman/Beck monstrosity at QB still ranked #14 in the NFL in passing.
I think Shanahan's lack of success can be directly attributed to lack of quarterback. I don't see Manning being worried that Shanahan is not a good coach, I see him being more intrigued by what Shanahan did for John Elway than anything else.