I'm sorry, but as someone who works in the field.. I'm still rather shocked you would advise that.
I agree, if someone is not technically able, they should not tinker within the ETP absolutely. All for consumers doing their testing before adding a callout to chorus, but advising the customer to potentially damage their device.
In the case that changing of the cable does work, ofcourse they are going to be happy and not continue through with resolving the actual issue at hand. That is quite simply bandaiding a fault.
Realistically the Yellow RJ45 cable that comes with the Fritz should be used, as realistically every DSL connection should be properly filtered and terminating that connection is by code meant to be a RJ45 Jack.
End of the day, in the long run at the end of the day... the Cost of the callout is generally cheaper than the Fritz and if the installation was done correct in the first place a callout wouldnt be required at all to get the connection working.