Acceptance testing for REST API

We have a situation to find Acceptance testing (SAT) for Webapi.

We are already doing SUT, and SIT. However, I am just wondering is it really a good idea to do SAT against Webapi or it makes more sense to hit SAT from UI level?

For me it does make sense to do SAT for non functional such as Security, logging, exception handling, performance etc..

But for functional level SAT, I believe it is going to be effective if it starts from UI because that is what the end user will see.

How others are handling the same?