Why is the man's wife worried about being sent to collections? She owes nothing to the hospital, the dead man's estate owes money. Let the hospital line up with the other creditors. She shouldn't be paying her late husband's hospital bills out of her own funds.
This isn't the same thing. Yes Gmail provides IMAP so you can read it from other clients. The issue here is that Gmail cannot use IMAP to ingest email from other accounts, as it can (or could) using POP3.
You're lucky he was referred to as Robert Smith. In my company they'd just have said 'Robert', and I wouldn't even be able to look him up in the directory to find out what the hell his job is.