It's possible they each put up with each other out of sheer amazement that the other one tolerates them.

"I'm wealthy, I can afford to pay you... whatever you need." He waves a hand vaguely, shifting off the doorsill to catch the teakettle as it whistles. Within a few moments he is returning to the living room with a small tray, carrying sake and tea. He restrains the urge to give vent to another brief coughing fit until it is all safely on the table, then sits with a very quiet groan. There's never a good time to come down with a cold. There's a soft clunk as he puts Ichi's mug of tea before him. "Ow."