Should Travis use "make distcheck"?

I just noticed that we had broken "make dist" on master, because one of the jenkins builders wasn't passing. I fixed it with 197d1992dba2fe.

Should our Travis builds be reconfigured to use "make distcheck" instead of "make all && make check"? It takes only a little bit longer, but it would help us be sure that we weren't running into any issues like the one above, or #25732 (moved).

Instead of passing things to "configure" directly in this case, we would need to use the DISTCHECK_CONFIGURE_FLAGS flag to set the configuration options that distcheck would use.