To the OP, if BT want to do the visit then it is unlikely you will be charged, I have had several visits in the last few years where a fault wasn't found at my property but either the exchange or cabinet. They weren't severe issues I should say, more to do with sync. I have yet to hear of people being charged for an engineer visit if the problem is genuine (even if not immediately visible), it seems you do need a visit from Openreach to have all of your line and equipment from house to cabinet looked over. Whilst I am in no way saying people don't get charged, that is usually reserved for the more umm techophobes.
Take the plunge, if they are recommending a visit from Openreach then there is clearly a fault, personally speaking I would find it highly unlikely you would be charged, again if your equipment is stable/fine then it isn't your fault is it?
Regards
John