If you don't have source address rewriting, and we assume that ingress
filters are in place (which seems the by default assumption) then the
source address selection actually determines the exit path form the
multihomed site.
Not in today's networks. Currently routers route on destination address,
not source address, so the destination address selection determines which
route is used to route the packets, which in turn determines which source
address you have to use if you want your packets to get out.