He said he marked the module before he sent it and the same module came back, but was not repairable.
You cannot be sure of anything! The ABS 'Module' has three parts 1) The pump motor, the round black thing on the end, 2) The aluminium silver hydraulic valve block with d.c solenoid valves and 3) The black part with the multi pole connector that's a housing cover for the VERY complex electronic control board.
1 & 2 are probably interchangeable between modules as long as the integral pressure sensor is o.k. But the electronic control board containing the firmware has the personality software and is what is programmable or may be able to be flashed with firmware. If anybody marks the outside of the assembled module and you then hand it over to a rebuild firm, you have no idea whether the important electronic control board inside is the same, has been replaced or been returned damaged and in a worse condition? Rebuild firms can easily check the pump motor, pressure sensor and probably keep a number of used controller boards. Boards like this usually have a hardware ID and version reference on them. That means the circuit and chips should be the same and only the flashed firmware can be different. I doubt the have enough info and skill to repair and test them. I have learned that on later models like your 2010, you can get the control board separately which makes a cheaper repair as long as the integral pressure sensor is good. The Dealer has to consider 'possible variants' and work through a list of part alternatives for different setups e.g is ESP fitted, is it a stop start EOS version or has brake energy recycling?
When vcds does adaptation coding it's only changing a few 'user' parameter variables. On brake items such as this, there will be critical parameter values which I don't think even dealers could change. E.g a brake pressure sensor may be fine tuneable to allow sensors to be calibrated, but functions critical to the timing and operation of ABS would be Taboo.
As I tried to explain, if you had your car towed to the dealer without any misleading or incorrect ABS module fitted and all the hydraulic lines disconnected and plugged, they should be able to source the replacement from your VIN and build information? By leaving a part there that may be incorrect, they do what most mechanics do first and start looking to replace what's there with a part that's compatible. This can waste a lot of time ordering and opening a V.W QA'd and sealed spare part costing them a fortune which they can't return!
The last line is a reason why you may be being told porkies - They don't want to take any risks ordering the wrong part and you've made it harder for them by creating uncertainty? Why not phone another V.W dealer, give them your plate reg. and VIN to see what part they offer you? You won't like the retail price, but at least you get a second opinion on the correct part and whether it is an upgrade replacement or not? Those kind of parts may come with specific dealer installation instructions noted on their parts list.