The issue isn't so much that module-starter adds a use Test::CheckManifest to t/manifest.t;
rather, it's that you added Test::CheckManifest under PREREQ_PM in Makefile.PL
(module-starter doesn't do that).
I was questioning the inclusion of Test::CheckManifest in Makefile.PL, not its presence in t/manifest.t.
I could tell (by inspection) that Test::CheckManifest in Makefile.PL would be a problem:
I force-installed Test::CheckManifest to circumvent that issue.
Take a look at "Re: Perl tools for making code better" for an example of my equivalent of manifest.t,
along with some related information.