Let's put this together:
it is a big market-research/polling type company
in a phone interview
I was not allowed to ask questions
(which latter one would be the st*pidest, redflaggest thing I have ever seen btw., ...unless...)
What if I told you, you had never been interviewed for a job?
You had been researched / polled; or more precisely, information about you had been harvested.
I offer this as I have recently came across a job ad active for a similar company where the job title was "Unsolicited application", and where — as far as I can recall — the job description was some pleasantly colored generic fairy-dust (requiring no qualification (again, if I recall it correctly)); something one could easily say to: "Well, with a stretch, I can see it plausible me having a chance at it". (Which further contributes towards drawing in a large number of people.)
So yeah, what if they are preying on the unfortunate of the job-market, and just abuse the landscape to siphon up the information they want? I offer you this possibility.
Let's look at the specific question in this light:
Do you like spending special time with coworkers?
Looks to me more like an item being part of some sort of poll, possibly sculpted a bit to appear more like an interview question. On this ground I would suggest not worrying how to answer this specific manifestation of it in an authentic interview context.