First time I've ever heard that one!  It's possible if the positive one
breaks, it could short out somewhere and set the car on fire.  However,
it should be obvious if this is about to happen, and I've never seen or
heard of it.  There basically no chance that a cable failure would hurt
your starter or alternator.  I'd say avoid that dealer like the plague!

The dealer should have taken the cables off and cleaned the ends and
made sure there was good solid contact.  The only time these large
cables have any large currents is when starting which should be for just
a small amount of time.  If there is sufficiently low resistance to
start the car, then the resistance should be acceptable.  You can check
for yourself by touching the cables to see if they are warm, especially
after starting.  If the engine does not turn over very well when
starting, then there may be a problem.  I have never heard of it harming
a starter or alternator.  Like Mike said, it could start a fire it if
came apart.