Correct. The difference between FPTP and PR systems (Or countries with very strong regional parties) is that in a multi-party PR system, the coalition happens between party, in a FPTP two-party system, the coalition happens within the big tentpole parties.

There are many reasons for why two-party FPTP sucks, but this phenomena is present in multi-party systems, too. And, of course, sometimes politicians end up crossing the aisle, much to the chagrin of the party whip.