[maxaf]

Considering how much brouhaha there has been recently in the media (legitimately or not) regarding privacy issues, I doubt anyone expects true privacy when using SaaS products or any old websites these days. There are obviously those people who really care about privacy, however those are a minority and probably aren't worth worrying about in your case.

I think making this work well (assuming underlying tech is solid) is a matter of UX technique. Iterate on a solution that makes the user aware of your support capabilities, then make it easy to summon help. Perhaps it'll be more natural if the user must initiate each support session, i.e. by highlighting a section of their screen and twiddling a control which makes it clear that human help is on the way.