I always thought Captain Kirk was lying about that. He was being bribed and what better way to confuse the briber than deny the value of the bribe. Kind of like, take your gems and stick them, somewhere.
Although you can't deny the Enterprise had very good manufacturing capabilities, from flintlocks to ultraviolet satellites, they were able to produce many of the things they needed.
Today gem quality diamonds, gem quality corundum crystals (rubies and sapphires), and gem quality emeralds can be made. I don't know if a starship's labs would have the capability to make gems - they certainly can't make dilithium crystals - but any major advanced planet should be able to make synthetic gems.
But today natural gems are more expensive than synthetic and if that is still the case in the era of TOS large apparently natural diamonds from an alien world would probably be worth a fortune if of gem quality - if I remember the size and number correctly, possibly the equivalent of millions of 2018 dollars, to say nothing of the value of being the only objects humans would be able to take from any Metron planet for the next thousand years. So I kind of hope Kirk took a few back to his ship.