proof of leaving the country is a standard requirement airlines often impose. They can be made responsible for flying you back if you're denied entry. It's been like that for a very long time. And some countries also ask to see proof of leaving. If you want to know which ones you'll have to look them up.
he said they told him to buy "return ticket" so maybe no proof of leaving the country? Like most countries it's usually a requirement if you have no visa.
you applied for a visa at an embassy but on entry you didn't check they'd used it for your entry? Did you show them your visa, in case they were unaware?