So in the end we have to agree to disagree and can only take the following from the information shared above, which is:
We still know very little about Pulse8's network and can't be sure of who they use to provide their service, they might use TalkTalk, they could use WBC where TTB LLU isn't available, it could be mixture depending on products..
Pulse8 also seem to release information thats seems to be wildly inaccurate, which isn't too good... but others do that too so
The issue could be anywhere really but one thing for sure is that their is no "BT" fault that should be affecting Professors service unless Pulse8 have been less than honest with him.
WBC @ 4500m > TP-Link TD-W8968v3 *Ceasing Soon
FTTC @ 450m > HG612 > Asus RT-AC87U *Migrating Soon BQM
FTTN Coming Soon