The founders of the company were invested in privacy and PBD, and we put a lot of effort into balancing data with privacy. One of the founders even spent a great deal of time on the initial implementation.
This work started years ago and I can say that everyone was interested in privacy, from recording/playback engineers to execs.
This was years ago too so maybe it has changed since, but my issue is with the whole premise of products like Fullstory that make it possible to essentially watch your user's over their shoulder without being given proper notification that level of monitoring is occurring.
I no longer work at FullStory, but I believe very strongly that the culture of privacy still exists.
Senior individuals at FS, myself obviously included, felt very strongly that we wanted to avoid any of the creepiness factor, and it was important to us that we felt comfortable with the technology. Discussions on privacy were paramount in all designs.
Anyway, Ublock blocks Fullstory's JS from running by default so at the very least your ad-blocker is potentially saving you from this level of intrusion.