If they don't agree and the issue is big enough for me, I'll find a new job.
So if the cheapest ticket is X dollars and the ticket you buy is Y. The employer will reimburse you for X and you pay the Y-X yourself.
Nothing illegal about that, it's the same as if a company says they will reimburse you for half your gym membership. You pay half the company pays half.
They can't expense a random "market price" but an actual ticket, if you then upgrade it it's fine, if you just say airline a had it for 200 and airline b had it for 300 and you can't expense the cheaper one.
However, if your company has strict policies about receipts and expense amounts you can always do the slightly shady "book two, cancel one" move - book one seat at the cheapest rate and another that's actually comfortable, print the receipt for the cheaper one, then cancel it within 24 hours to get a refund. I don't recommend this of course, but it is a way to get around excessive red tape.
(a) being crammed in a space uncomfortable for anybody over 5'2" or 120 lbs between two chatty salesmen mutually disapproving those who think the world is ca. 600,000 times older than they think it is, or
(b) being shot with a tranquilizer dart and shipped in a dog crate.
I mean, I'd seriously consider (b) before sighing and going for (a) + alcohol.