Sure, but I assume there's something in the device itself that indicates there is a profile or remote access? I don't see a work-related profile on my phone, but maybe there's something else beyond the obvious Profiles entry in General settings?

This is why I frame this as an ethics issue. If you install some sort of MDM profile, unless you spend a lot of time understanding mobile device management implementations, you won't necessarily know what the capabilities are.

If it is your device, typically an employer will disclose in their policies what capabilities they use.

Now, does this prevent a rogue infosec person from deviating from the policy? No. Nor does it prevent the state from compelling the company to abuse their MDM technology. If these examples are part of your threat model, you should not use your personal device with your employer's infrastructure. I don't think this makes your employer's choice to use MDM a bad one, however. They are protecting the corporation, after all.

> Ask.

This is a good recommendation.