The demarcation between 'network side' (not your responsibility) and your wiring is the test socket. If there was a fault in the back of the NTE5 master socket, that's not your responsibility and you should not be charged. If the fault was with extension wiring connected to the NTE5 faceplate, that is your responsibility and you were correctly charged.
I am in dispute with TalkTalk with a similar issue.
Earlier this year, I lost my telephone connection at regular intervals. The fault was intermittent and from time to time, I could not make or receive voice calls. My phone did not ring and anyone who dialled my number received the engaged tone. Broadband speeds also fluctuated significantly.
I received many visits from BT Openreach engineers. However, up to two days can elapse between the initial fault report and arrival of an engineer. By then, normal service seemed to have resumed (of its own accord) - and diagnostic tests did not identify any fault. However, I noticed that the problem appeared to be weather related, because every time I lost my telephone service, it was raining heavily with driving wind.
BT engineers persisted with their diagnostic tests (to no avail). Eventually, I lost my patience with TalkTalk. After two months, I insisted that an engineer should climb a ladder to inspect the wire that led from the telegraph pole to my house. He quickly discovered cracked insulation on a wire, which was stapled onto an exterior wall of my home. That wire ran from a junction box to the master socket inside the house.
My telephone service used to be "star-wired", with an old-style master socket (not an NTE-5 master socket). Consequently, the engineer decided to fit a new NTE-5 master socket in a different location. He also ran a new wire from the telegraph pole and left me to re-connect all of my extensions to the new master socket.
I thought that was the end of the matter. However, three months later, TalkTalk billed me £50. When I queried the charge, they told me that the engineer's notes stated that the fault was caused by a problem with my internal wiring.
The cracked insulation was definitely outside my house. Furthermore, it was on the wire that led to the master socket. However, TalkTalk have washed their hands of the affair and say they can do nothing. They don't seem to realise that after months of appalling customer care, they are encouraging me to switch to a different telephone company. I shall do so, as soon as my 12-month prepaid line rental expires towards the end of this year.