Can HR at another company report of the possibility of me renegeing?

I accepted a job offer from Company A investment bank and signed all the agreements. But sometime later Company B investment bank calls me and asks the usual HR shit. I accidentally emailed an updated version of my resume that had the job at Company A on it even though I hadn't started yet. At the call: I said some stuff that technically wasn't false but maybe misleading. Realizing my mistake, I emailed her a couple hours later saying "I just accepted an offer in the area of Company B but would be open to seeking out new positions in the coming months."

If Company B went apeshit and notified company A, will they rescind my offer thinking I wanted to renege? FWIW: I had a few concerns about Company A and Company B supposedly will pay me a little more.

Company B is in Chicago and Company A is in NYC, so low likelihood that anybody at B knows anybody at A...I think