"Demand" really means "demand at this price". That's why there's a demand curve - the amount of demand changes as the price changes. So, no, the pool of candidates is not "genuinely smaller than demand". The pool of candidates at this price may be genuinely smaller than the demand at this price.

What I think is happening is that companies are offering less than the market-clearing price for talent, and then complaining that they can't find talent (at that price). Well, yeah, that's usually the way it goes when you offer less-than-market prices for anything.