Whether they specifically needed the X21 rather than the 21 or X12 or not would depend on where they were going on the other side of Durham.
They also might, mistakenly, have been under the impression that the 21 takes a lot longer to get into Durham. I hear a lot of misinformation given out, even by drivers. Online route planners are no better. They sometimes only tell you about one of several equally viable options.
Re: specific prices, it's only £3.10 for a GNE Durham City daysaver or £12 for the week - that allows travel between Pity Me and Durham city centre. The Arriva equivalent is £3.60/£13
https://www.simplygo.com/town-and-city-fare-zones/
RE: Pricing