He's Matthew Linus. He's one of the top ten richest men in New York, in the top 50 of the world. He should not be standing in disguise in a 24 hour dingy laundromat, doing his own laundry like some ordinary citizen.
And then she comes in, wearing what are obviously her 'laundry day' clothes, big orange headphones, and a smile brighter than the sun.
Most of his clothes are 'dry clean only', but when did anyone actually listen to those tags, anyway?