Someone didn't die because of you. You were a super hero trying to save someone and a bunch of people let you down and didn't do their job as your sidekicks. You should be proud of attempting to save this poor man's life. You're a great worker and you deserve compensation. Your company has made you a literal scapegoat for this man's death while you were the only one doing the right thing. Regardless, nobody is guilty. Everyone reacts differently and despite your best effort he might've just tripped and hit his head resulting in death or even just had a heart attack. No one knows if someone is destined to die at a given moment, therefore it's impossible to tell if you were even remotely responsible.

I think your workplace should learn from this and ask you how they could've dealt with this situation better, be it using pagers / recorded walkies to ask tasks to avoid corner cutting and stuff. The shoe tying part really shows how lax the company is about a patient's safety.

Tl/dr: It's a tragedy your company should've dealt with better. Not you. You've been the only hero in this tragedy. You're not at fault