Now and then this eccentric idea comes out. Frankly we can't see any rational reason to understand how from an amount of connections per user which can be stored into single integer variable one should jump to the idea of logging.
We operate servers of our property as well as rented servers. That's another bizarre idea, which you use to jump to conclusions. Anyway if you think that a datacenter logs the traffic metadata and/or content of any and each communication to/from the devices using their lines, what is the difference between an owned and a rent server? By the way just apply partition of trust, end of the story.
Kind regards