I appreciate when "Woe is Me" style comments are knocked down a notch when they conveniently ignore half of the world. The activity surrounding the discussion is indeed using networked applications, of which the web is only one.
So I don't think they were being needlessly pedantic, nor do I think they didn't understand what the parent meant by internet in the colloquial.
Lots of different ways one could take this: maybe whom they were responding to is just being lazy, that the good parts of the internet are there for them to explore, but they are beholden to their web browser and their favorite loathed platforms that 'make the internet suck'.
Or maybe whom they were responding to really has gone the rounds and really has considered all the options and bemoans how difficult the non-web internet services are to use, and how inelegant they can be at times and what a pain they are to maintain if it isn't your full time job.
There can be so many ways to take written material on the internet; more often even pedantic comments at least let us ensure we aren't simply reaffirming our own biases.