You are not referring to the status of each file operation ('file operation's status'), nor are you referring to status of several file operations (file operations' status).
You are referring to the overall status of some function you've labelled as "file operations".
Consider the following:
"What is your job status?" This is OK, but some people have a few jobs, so "What is your jobs status?".
The question is not asking about the status of any job. It's asking about the status of one aspect of your life, labelled "jobs". Basically it means "Do you have a job? etc.", not "Do you have a rewarding, well-paying job?" - ie. the status of the job/s.
In any case, I think you (or your colleagues) or being confused by the "s" on operations. The same argument should apply to singular nouns. But you say "What is the "free memory status" of your computer at the moment, not "What is the "free memory's status".
You say "What is the battery status?", not "What is the battery's status". You could say the latter, but it's not necessary.
Since there's no need to use a possessive on these singular concepts, there should be no need for it just because you have labelled a concept as being plural. It's a red herring.