The modules concern is'nt that a hosting provider doesn't let you install modules. Those providers should never be even considered. It's that some hosting providers have methods for doing so, but that their methods create unpleasant overheads. Some let you install modules for the single site itself, but then you have to do bugfix updates for every site individually even though they're on the same server. Others will let you request a module to add server-wide, but they make you request each one individually or take a while to give the response. Still others let you install in one place for all your sites without interfering with other customers of theirs even without a VPS or a full server, and that's great. A VPS or full server hosting arrangement of course shouldn't pose any problems.
The advice to keep an entire application together in one place was actually an article published by O'Reilly on Perl.com several years back (2001, to be exact). It's this one, written by Jesse Erlbaum who is referenced many times on the project's web site (often by first name only). Now, I'll admit that web applications have grown on average past what was expected in 2001, and the advice makes more sense for small, simple applications than for larger, more complex ones. It's good to know you don't recognize that advice, because I'd hate to think it's still being given. It's bad enough it was given then.