Far be it from me to inject a real question into this thread, but here is a real question:
In our normal base 10, we have a protocol for SPEAKING large numbers, so 154 is "one hundred and fifty four".
Using the same logic, what would be the generic method for similarly SPEAKING large numbers in other bases?
IMO writing and speaking are two different things. Words don't mean anything, except the meaning we give them. Spoken words are sounds that represent ideas. Written words are symbols to represent ideas. Neither spoken nor written language has any inherent meaning. Otherwise we wouldn't have to learn how to speak/write other languages. "15" does not mean "fifteen" just as it doesn't mean "0x0F". However, from a mathematical point of view, when talking about the numbers these symbols/sounds represent, 15 is equal to fifteen is equal to 0x0F. Therefore they can be used interchangeably. Since (to the best of my knowledge) nearly all humans use base-10 when speaking numbers, it would be correct to pronounce 0x0F as the base-10 equivalent (15) in the language you are speaking.
It's all just a different way to say the same thing. We encounter the same issue in spoken languages as well. I might say "fifteen" but someone who doesn't speak English will have no idea what I'm talking about. Or even if someone does understand English, but the rest of the conversation is happening in French, someone would be understandable confused if I suddenly said "fifteen" using a different language.
In other words, use the language you will be understood in, as determined by context and requirements (obviously you should say/write 0x0F if you're talking about a computer data type that must be in hex) of the overall conversation.
Of course, part of the point of a riddle is to be tricky. And saying "ten" when you're talking about "10" in binary is intentionally misleading, not to mention technically incorrect. That's why it works better as a written riddle/pun. Because you're not giving yourself away that you really mean "two", e.g.,:
There are 10 kinds of people in this world: Those who understand binary, and those who don't.