And how do you know I've created a problem? Is that the only possible explanation?
I don't, but that is irrelevant. If the issue is with the provider/Openreach kit there is no charge. if you have created the problem you will be charged. Not rocket science.
I want to know what constitutes a "fault" before I know whether to accept the risk of getting them out to 'look' at it - what will they look at and consider as faulty - but nobody can tell me that. So for all I know they might just run the same automated test, perform a quite line test on a nice dry still day with no noise, tell me there's no fault, piss off and send me a bill. Next day it rains or the wind blows the wrong way and nothing has changed except I've got a big bill.
I still have enormous fat twin core cable running down the front of my house too which I think is long obsoleted. I think it's joined somehow to the overhead run of newer stuff. Maybe that's where a fault is, maybe it's miles away, but I don't know if it'd get changed regardless just by virtue of its age or possible fault condition. Nobody can tell me, so nothing has ever happened. I don't really use the phone anyway but that's beside the point.
If you ask them what is covered and not then you will be told, try it. Simply put though, if the issue is on the exchange side of the main BT socket then it is provider/Openreach, if it on the premises side it is your issue. The cable you mention will be exchange side, so anything there could only be charged if they could show you had done something like cut it when gardening for example. If you haven't touched it then it is their responsibility
Some people are obsessed that they will be charged for any call out at all, that simply does not happen. If they do charge when you can see that it is on their side then dispute the charge
I don't see how this fits with your analogy.
Because is both cases you pay for someone to provide and maintain equipment, and in both cases they repair anything that goes wrong with their kit without further charge, but will charge you if you call them out to fix something else.