My last company (a well know credit card Co.) once introduced a system by which business trips where to be flown with the carrier of the country visited (apparently as a courtesy to the people we were visiting but actually for other reasons not pertinent to this thread).
In my team we complied in as much, to give you some examples:
To Germany, we took Lufthansa no problem
To Switzerland, Swissair (At the time), no problem
To Israel, El AL, no problem
To Italy, err..., British Airways! Somehow the Alitalia flight times were never convenient to us
I've flown once with them, never again.