My problem with Invision, which we used extensively about a year ago to redesign POP.co, is that it expects you to live in its own interface and interact with the Invision prototype on their own terms, inside their walled garden of sorts.
This is OK, and kind of makes sense in the app-driven world we live in, but to really fit into the kind of hectic, ten-different-tools workflow that we thrive in at the office, screenshots are the core lingua franca.
We can attach them to Pivotal tasks (or Hipchat convos, or anything else), forward them around (even via SMS!), scribble all over them, print them out and stick em on the wall for a meeting.
With Invision, we'd be crowded around a phone or screen, and unable to interact with the collaborative output in other tools. I came to dread receiving an Invision link in my email, especially because I couldn't tell which shortened URL referred to which project.
Overall, I've come to really hate tools that expect me to live inside them, rather than them living inside everything else I already use. I don't want to leave my flow.
Hope that made sense. :)
There's also a larger lesson to be learned about finding the integration points that make the most sense to the application you're building. Things like email and calendars are obvious, I wonder what else should be considered from the same point of view.
Rather than the sense of dread you mentioned, I just let other things take higher priority than the emails with Invision links. I thought it did work well when a designer led a small group through a prototype live.