However, the manager of the other group should get some management training. He did a piss poor job at communicating. All it would've taken is explaining the group's prioritization and roadmap and the OP would've not left with "THIS COMPANY CAN'T DO SHIT!" feeling.
Now, if they don't have a roadmap, and their prioritization sucks, that's another matter, and entirely possible, of course.
My impression of the OP is that he expects other teams to drop everything and make the change. He may have been told about the roadmap but feel that his project is more important. That seems more likely than the following excerpt from the post.
> So I reach out to the manager and ask what is going on. This is a simple task, I said. Why does it take an entire quarter for your team to deliver? He doesn't have an answer.