He has the authority, but also the obligation. If a Catholic (and this woman is supposedly fully initiated) is properly disposed (i.e. contrite with a firm purpose of amendment, no reserved sins or censures) and makes a reasonable request for absolution (she came during the scheduled time!), the priest is *obliged *to grant it. Now, this is all supposing we have the details right, but you can’t ascertain whether those conditions have been met without actually talking to the penitent. I can understand the priest hearing about fishy marriage and decades away and thinking “this is more complex than I can handle right now,” but that doesn’t justify brusquely turning away a penitent without explaining that reason, let alone making up some spurious claim that the penitent is no longer Catholic (she would have had to formally defect, basically with a written notice to her bishop, for this to be true).
The OP is correct that for someone not operating under some form of canonical censure (like excommunication), all that is required for reconciliation with the Church is sacramental absolution. On that point he was right and the priest was out of line. If any parishes do place other obstacles in the way, no matter how prudent and useful they may be, my guess is that when push comes to shove they could be bypassed. It is not within the priest’s purview to add more burdens than canon law provides for.