"Acceptance Test" is an oxymoronic term. Furthermore, it contains two verbs (only).
Let me refer to some definitions found on Wikipedia:
Acceptance in human psychology is a person's assent to the reality of a situation, recognizing a process or condition (often a negative or uncomfortable situation) without attempting to change it, protest, or exit.
Software testing is an investigation conducted to provide stakeholders with information about the quality of the product or service under test. A primary purpose of testing is to detect software failures so that defects may be discovered and corrected.
In those two definitions I recognize the oxymoronity of the “Acceptance Test”: Investigating reality of software without attempting to change it, with a primary purpose to detect failures so that defects may be discovered and corrected.
I have experienced several situations where this conflict has occurred. The project management saw de the acceptance testing as a part of an acceptance process where the customers had to declare the product (unconditionally) acceptable. The same time, when we, the testers, organize an acceptance test, we are leading the customers to look for problems (risks) to declare the product rejectable -unless the problems are resolved.
The question remains: is an “acceptance test” an acceptance or a test process?
I do agree that the “Acceptance testing” as described in your post is very important accept is should be called something like “customer testing” or “user testing” or whatever. As long there is a noun and a verb and not two verbs.