Roseway's reply is very close to the mark. primaraly the filter (be it the micro filter you get for each socket with some apperatus plugged into it or the full face plate you have) is mainly trying to filter the sort of induction (radio) signals similar to broadband from your broadband.
Other erronious voltages, short circuits etc can also be upsetting the dsl signal regardless of the filter as this isn't what the filter can guard against, so you may have some apperatus plugged in or a fault on your internal wiring which causes problems on your connection. It may even be a faulty front plate (lightning,damp, physical blows may be the cause here).
If you get a difference with front plate and test socket - would disconnect the inenternal wiring from the front plate to see if its the plate,
If not reconnect the internal wiring and dissconnect all apperatus, next step if it's apperatus, plug each one back in one by one till the problem reoccurs.
if its the internal wiring then first have you got more than one lot of wires in the face plate then re/dis-connect one lot at a time. If this reveals a suspect or you have one lot of internal wiring comming away then find a socket junction box mid way and disconnect here and keep repeating until you can identifi a suspect lenght, then you can either inspect this bit or replace it any way.
Your normal telephony works differently, actual + and - voltage on the line. your telephony works like your speaker wires. Broadband more like a radio signal trapped within the wires. (the router/modem is like a radio which converts that signal to something the computer can hear as a radio converts radio signal to something you can hear. Only unlike dial up the modem is listening to lots of radio stations at the same time and blending the whole into one vast mush of info for the pc hence the expresion BROADband.)
Dispite working this way, any other conditions thrown on the wiring physicaly can also affect the dsl. your ISP may be getting some sort of condition on the line when requesting a line test. Only thing is it your wiring or in the net work
Phew can I do war and piece