Fiesta brava

I've viewed this film over and over and my piano training says there's no trick photography in the scenes where Montalban plays Green's adaptation of El Salon Mexico. I'm sure the beat-up old piano is not the actual sound source, but Montalban is hitting all the right keys at the right time! His technique is well above average, and anyone who could even fake that well would have to be able to play well too. Yet there's no mention of musical skill or training in any of his bios, nor does he play in any later films. Can anyone shed some light on this mysterious aspect of the multi-talented Senor Montalban?