NYC Employer Claims Policy Disallows Restrictions

I work hourly as a dietary supervisor in a nursing home in NYC. I had an accident off the job. Came back using a cane and with a letter from my physician restricting me from doing lifting, bending, standing too long. I'm paid hourly.

They claim my use of a cane entails a liability and that they have a policy of not allowing workers to come in with any restriction. There was no discussion of modified duty, reasonable accommodations, etc. They told me I am forced to stay home without pay until a doctor says I can work without any restrictions. Is this legal or do I have a case? They're goading me into temporary disability or unemployment.