The passports don’t matter in this situation, the Governments of both Greece and the Uk have procedures in place to deal with emergencies like this .
Remember his password was scanned when he checked into his flight to Greece and then again at Rhodes airport . The tour operators have all the details in their system too.
He and his family can be easily identified from this, plus information they can provide such as NI number, date of birth , address etc .
Remember the Greek authorities want the tourists repatriated just as much as the tourists want to get home. Everyone will make things as smooth as they can.
Your DB did absolutely the right thing to follow instructions and evacuate as he did. No one knows what could have happened if he had take the time to return to his room . Many Resorts on Rhodes are spread out over a wide area, it’s quite possible to be on the beach / pool and be a 5-10 min walk from your room .
At best he could have been separated from the rest of his family and they would have all been distraught. They could have ended up on an other bus or hotel at different locations.
Sometime people fall and get crushed or injured trying to enter a building when others are leaving in a panic.
Passports are very easily replaced ( I've just done it ) when they get home, as are clothes and suitcases and their insurance will cover the costs. It’s actually much easier than many other insurance claims as most of us have a list of what we packed and also usually don’t take items of sentimental value on holidays .
Most people just take passport / bank cards / cash , clothes , shoes, toiletries and electronics / books . Money can easily replace all of these.
Please reassure your brother, all that matters is that they are all safe and well.