She's been apologizing for being a bother repeatedly, though, so that might be less about national customs and more about actual personal anxiety.
Also, I too used to think not causing trouble for others was a way to make people like you, but instead it only makes it easier for them to ignore your presence.
You're right, of course, but I'd argue that this point specifically is a reflection of the culture of the author rather than an intentional depiction of her anxiety. The fact that she said "no" so bluntly, sending Hitoyoshi into shock, is obviously meant to be her fault, but her continuation afterwards, which he misses due to the aforementioned shock, is meant to show that he misunderstood her. She was not saying "no," but rather doing the obligatory "I don't want to impose on you," inviting him to ask again. Classic misunderstanding.
Also, I think that you should avoid viewing this cultural norm through the lens of your own culture. In the west, yes, if you repeatedly answer "no" whenever someone offers to do something for you for the first time, that will be taken as a "no," and eventually they'll stop offering to do things for you. But in Japan, everyone knows that they're supposed to ask again if they're serious. The same thing won't happen unless you repeatedly answer "no" the
second time, as well. It's a different culture.