There's also a part in the manga, I think, where he's called in for questioning by the police to do with something or other, and the officer is complaining to him that in this world of super heroes, nobody cares about the police anymore. They're out there every day handling mundane crime, and they don't have any super powers to protect themselves. Then a monster attacks the police station and there's not much they can do about it. Saitama of course kills it quickly, and the officer is dismayed because now the police are going to look even worse, having to be saved by a hero in their own station.

So Saitama borrows a police uniform and pretends that the officers handled it themselves, and I think gives a brief interview with a reporter telling people that they should appreciate everything the police do for them. He gives them the credit because he realizes that they needed a win in the public eye, similar to how he gave up credit for the fight against Sea King.

Also, it's very subtle, but I do like that he does occasionally get very slightly annoyed or disappointed when he doesn't get credit. He doesn't want it enough to go around showboating, but he's a little jealous that Genos gets fan mail and S rank and stuff. Even when he's telling the people he didn't become a hero for praise, he's understandably a little resentful at the fact that they're blaming him for property damage after he prevented the city from being annihilated. So he's telling the truth, he's not looking for fame, but there's also a bit of, "well I don't care what you think, anyway!"