if you cut a muster, presumably you do not attend it

Assuming that that is what is meant by cut in this context, an assumption that I do not feel is entirely warranted. Merriam-Webster offers this definition in this context:

to be able to manage or handle -- usually used in negative constructions <can't cut that kind of work anymore>

This would make cut the muster all the more likely; to be able to show up ready to accomplish a job.