At what point were they having you send the money they just sent you back to them, but in a different form? Did your company have you wire to some random bank account? I assume not. These are not the same scenarios at all.

For one thing even if the company never reimbursed you - it wasn’t an outright scam, you did get a flight. The scam scenario you are literally just sending money to a scammer - with the extra flourish of getting a fake check.

What you say about expensing is not unusual and there a number of reasons for it. It does offload the onus of correctly making reservations, putting in KTIN and immigration info on you. And then the big one is that I get all the travel card benefits (points). I even prefer it this way.