What about someone who works for a bank but banks at another bank? Should they be fired? Or maybe they just don't want their personal financial information available to co-workers.
How about someone who works for a slumlord -- or "mobile home park operator" -- but, lives in a nice home in an upscale community?
Shall they be forced to move into the boss's digs, or else be fired?
Twisting arms inevitably leads to resentment. The more they screw with the workers, the more the workers will screw back with them. Creating a "hostile work environment" -- an "adversarial system" -- tends to result in some natural repercussions.
The "Land of the Free" was formed by people who didn't LIKE being told what to do. And frankly, "Because I Can!" is something that may work for BJ Clinton -- and, "in a court of law" -- but out "in the hustings", all it does is piss people off, when they're shoved around, and the "shover" tells the "shovee" that "I'm doing it BECAUSE I CAN!"
Do they have the "right" to do that to their workers? Well, maybe. Maybe even "probably".
Will their workers resent it? Figure that one out for yourself.
Will "resentful autoworkers" be "an asset to the corporate bottom line"? Ask the auditors. Or read the business section of your newspaper.
Good grief.
Your example with the bank is hardly apropos.
You are a Ford employee parking your XYC car in the Ford lot. Your banking affiliation isn't in anyone's face, much less your employer's.