The BV can't see that, anyway. They can only see the IP hash. If they reset their IP, then their hash doesn't change. The only "super view" that the BV has is that they can see the board IP hash, not just the thread.
Since I phone fag, if I reset my connection, the tower will assign me a different IP. I have noticed that the towers actually have an IP range to them, as there are certain towers that are likely to give me an IP that is banned, and it is the same banned posts from those towers.
The BV can't see if I force a new IP from the tower, or happen to switch towers. What the BV can see is the same IP hash any time an IP address makes a post to the board. So if I were to go post in another bread, BV can see it.
BV has no earthly idea who is or is not hopping IPs. That is precisely the purpose of a VPN or the like. The sites you interact with don't see your computer/phone, they see the VPN address. Same with all ISPs. They assign an IP to the customer's internet connection and how they do that may vary, but for some which have a dynamic protocol, they may not have a fixed IP address for the customer.
But I digress.
BV has no such ability to identify shills. The fact he/she/it has tried so hard to establish that they are capable of this is proof positive of the decline of both board administration and the quality of anons.