I am sorry, but that is absolute bull5h1t.
What about the differing types/ages of the BT network.
0.32,0.4,0.5,0.7,0.9 and even 1.17mm cable,either copper or aluminium.
Using cat5 or cat6 cable will not make your broadband slower or affect the service in any way whatsoever.
BT/Openreach...