you're probably being paranoid, and yes, it's a coincidence.
All broadband services originate with BT - they sell the service to ISPs via BT Wholesale. If there's a problem with your connection, and your ISP says it's being caused by BT they may or may not be right. If they are right it's possibly an exchange fault, or something wrong with your line.
It certainly isn't somebody at BT deliberately slowing your broadband connection to make a point.