Both AMG and Rentech along with a few other tuners are getting into the diesel game as of late. Both make mods for the CDI's.
AMG was an aftermarket company back in the 80's. You had to order your MB then ship it to AMG. They would pretty much do anything from just a spoiler to a full DTM build. However
afaik they never did anything to any W123's. At least I have never heard of or run across an AMG W123. AMG W126's are around though.
To ID a real AMG car you need to run the vin, AMG keeps records. Also in the case of the W126's some of the mods are pretty extensive. From complete custom interiors to body kits, to 6L engines.
These days AMG still works with MB and builds a limited number or "real" AMG cars, ie not really MB's. Take the CLK-GTR for example, more AMG design then MB. They also build all their engines in house by hand. Every one is signed with a serial number. They do some really exotic stuff, like the 7.3L M120 V12's with titanium valve trains for Zonda. Of course they also work very closely with MB to build the fast cars we all know and love, that you can buy right from your local dealer.
There is an argument as to how modified the car has to be to have an AMG badge on it. I am from the school of thought that unless you have had engine, driveline, suspension, or brake work done an AMG badge doesn't belong on the car.