Of course not, the alternate is writing these projects in a more maintainable language

It's not exaggerated. You can spend a couple of days rebuilding it in a better language (and I have done that!), but what actually happens is people want new features far more than they want you to rebuild it in a better language. So in most cases it gradually grows and gradually gets more unmanageable and it gradually becomes more difficult to justify a rewrite. There's never a solid point where you have to do a rewrite so it grows and grows until you really really wish that you had but it's also way way too late.

Happens all the time in my experience. It goes so far that big companies like Facebook, Google and Dropbox have all ended up writing their own Python/PHP runtimes or even entirely new languages like Hack and Google's new C++ thing rather than rewrite, because rewrites become impossible very quickly.

That's why - despite people saying language doesn't matter - it is very important to pick the right language from the start (if you can).