IO-540
It's not correct to say that all you need is the CAA's file reference for a minor mod in order to incorporate the same mod to another aircraft. The CAA reference merely states the approval of a data package, but does not include that data. You need the actual data package from the original applicant in order to do the work, so you ensure the work actually complies with what was approved. That's why the avionic shop that produced the original data expects to get paid for it.
As an example, a CAA minor mod could have approved a transponder installation - say a Garmin GTX330 into a TB20. The CAA AD261 approval document (prior to EASA) or EASA Tech visa, would say just that. It wouldn't tell you were or how to mount the antenna, altitude encoder etc, or provide the wiring diagram, instructions for continued airworthiness etc. You only get this data from the owner of the approved data.
It's no different in the US system. You can't copy a 337 from one aircraft and use it again on another - you must submit more data - (it could be identical), to the FAA FSDO, or to an FAA DER, and get the inspector to approve it. If you use an FAA STC, you have to have a permission letter issued by the STC holder allowing you to use their data against a particular aircraft.