Is it possible for a crappy outdoor antenna to be better than a good mobile antenna? Sure.
Is it possible for a messed up install of an outdoor antenna to be better than a proper install of a mobile? Sure.
There are a bunch of reasons why what your friend is saying could be true. The most common reason is people splice extra-long lengths of cable on an outdoor antenna without understanding the losses involved in choosing the wrong cable. Other common reasons include improper, too many, shorted or corroded connectors.
If I thought my mobile antenna was doing better than my base, I'd be climbing the tower (or, more accurately, getting somebody else to climb the tower) to find out why, and fixing it.