In another thread, someone mentioned that First Republic did offer special conditions for leaving large cash deposits with them. I assume it's similar in this case, isn't it?

Essentially, you buy e.g. lower rates on a personal loan by keeping your company's cash with them, far beyond the insured amount. It's not just "I could've chosen any bank, I just wanted my money securely stashed somewhere", it's "I put my money here, knowing it's not insured beyond this amount, but I get favorable rates in return". The lines between deposit and investment get really blurry there.