I owe them an apology.
It isn't just Pekes.
It seems that other bracychephalic breeds can't do this either - notably many Pugs, French Bulldogs and Bulldogs. And, according to the many YouTube videos that come up if you search for "[breed] can't reach itchy butt" [what a way to spend a Friday, eh?], it's hilarious!
And there was me thinking it was a total bloody disgrace.
In the interests of balance, here's a video of a Pug that can - just - reach behind to help deliver a rather impressive litter of pups. Bizarre choice of music and OTT sentiment, be warned. But rather affecting, nonetheless, especially when Dad comes to say hello to his pups. Just such a shame they have no choice other than to be Pugs.