While I think it's important for workplaces to take care of their employees, I feel like Pete's issue was that he was too close to work. And on top of that, he wasn't even an employee, just a contractor with no benefits, PTO, etc.
The real problem here is that Pete was not integrated as an employee. If he were, he could have taken PTO, accessed health benefits, and gotten help. I don't know the complete story, so I won't extrapolate further, but I feel sad thinking that this team almost feels "responsible" for his suicide. It wasn't the remote team's fault for not catching on, it was the company's fault for not acknowledging the health and security of their contractors (who, I reiterate, should have been employees).
Don't mean to offend anyone, I just felt the way contractors are treated is sometimes unjust.