PSV Type in Superimposed Variable Back Pressure

I see no one has responded to this so I will try.

The simple answer to your question is that both vendors are right and wrong. The statements are far too general and as such could be dangerous if not well understood. You must have already come to that conclusion when you read Section 3.3.2.2 that you quoted. Vendor 1's statement is not always true as can be seen from your quoted section. Vendor 2 is possibly correct under certain specific circumstances but such a broad statement is not acceptable.

Some background: The purpose of a safety relief valve is to protect some piece or pieces of equipment from a pressure that is higher than some or other design Code allowed pressure. Back pressure is made up of two components that are additive, superimposed (which may be steady or variable) and built-up pressure which is the pressure built up while the valve is relieving (this could also be steady or variable depending on to where it is vented).

Back pressure has the effect of adding to the spring force to keep the valve closed. If you know what the back pressure is you can compensate for it and set the valve at a correspondingly lower opening pressure (see section 3.4). This is made clear in API, which you have somewhat misquoted by leaving out the first part of the sentence. This is the exact extract -

Section 3.2 is pretty clear, if you have specific questions feel free.

Remember to read all the other related sections, as none of these can be read in isolation. For instance you must read section 3.3.3.1.3 on the 10% limitation on built-up pressure etc.