Is Asian (...) culture like this? (...) the inability to say no?
Basically, yes. In both Japanese and Chinese culture, there is a STRONG cultural bias towards shaming the one who says "no" as "arrogant" or "rude".
t. got a Chinese not-blood-related sister
On the face of it, only. Like, if an older Japanese guy responded to a request by sucking in air through his teeth, that's a definite no.
Beyond that, as you get to know the culture, "Noes" become more and more obvious. Also requests. You won't pick up on requests at first, either, even though they know they have to be more blunt with gai(koku)jin tachi.
By the way, a lot of the manga here have coded language. You may wish for people to "come out" openly, but a lot of the language the manga uses is basically that.
At first, I leveraged that a bit to get people to go along with requests they wanted to say no to, but after I;d been around long enough to not be a newbie, that wouldn't have worked.
This is why I admire the translators on Dynasty, they as a group have a good grasp of context.