I... also have complicated feelings here.
To begin with, he started this manga WAY worse, to be honest, so a random guy hitting on her is really not THAT big of a deal. But at the same time, the guy was a douche. I hate the type. It's not that he hit on a woman he saw alone, and then backed off. He started speaking English, and he doesn't know Natori so he doesn't know if they understand, and makes the comment about how good she smells. And then the card? I know it's a very Japanese thing to do, but that's like the opposite of backing off.
And it's not like Natori told her off or anything, she asked. Personally, I think it's healthier that they actually air it out and not let it build up, so it'd been better theoretically if he'd just mentioned it. But anyway, he tried to be objective and impartial, even if he failed.
Also, it's not necessarily (or not only) that he doesn't "trust" her. We know Asako has self-steem issues, she LITERALLY doesn't know how this whole thing works. A dude might be trying to get under her skirt and she'd think he's just being nice.
I already hated it, and you're telling us this is just the tip of the iceberg? Boy, I'm not going to like this volume...
And this manga was going SO well... The little drama was well-placed, well-handled (and in a timely manner). But now it seems like...this is going to go sour. Fast.