Potentially Being Let Go From Company Because I Use A Cane To Get Around...

I recently started a job (Monday) for a Distribution Company on the west coast. During my interviews with the recruiter, she was informed that I used a cane to get around as I have nerve damage in my legs post covid. When I had my in person panel interviews at the company, I used my cane to get around and it was propped up next to me throughout the interview. Nothing was said or asked about regarding it, instead we just focused on my experience and time in the industry.

After being there for a week, mostly doing night work for a network cutover, I received a phone call from my recruiter asking me if I needed the cane to get around. I confirmed I did and that there had been no on the job accident that necessitated the cane. She said that we were good to go and hung up. Later last evening, she called back and asked me to get documentation for my cane use from my GP. I asked why and she essentially told me that she couldn't let me back into the warehouse without the documentation for my accommodation.

I'm not asking for an accommodation. I'm not asking anyone to walk slower, drive slower or excuse me from climbing on a scissor lift. I can and have done all those things this week. I'm also in the IT dept, so the vast majority of my day is sitting in a chair and typing... I was not drug tested or given a physical prior to my offer letter, which I also thought was strange.

To make matters worse, because of the state of American employment practices at this time, for my first 90 days with the company, I work for the recruiters company and not the Distribution Company itself, where I can be terminated for any reason. Do I literally have a leg to stand on ?