I have been in / heard of situations where refusing a drink could be considered mildly impolite--> rude--> deeply insulting. But it was almost exclusively in places where making wine/beer/other alcoholic beverages is part of the culture. Not the industry or the market, the culture. In such a community, alcohol consumption is a lot more that having a few kicks, it's a rite. Of bonding, mostly. And rites have rules.
For example, a toast may be a serious matter in that context. You greet or wish good health to someone, you "seal" the gesture by taking a sip or possibly emptying a cup (a rite, see?), and it's a lot like extending your hand for a handshake: you expect that person to extend his hand, too. So if he doesn't drink back to your toast, he is being terribly offensive. Sipping instead of drinking properly may be tolerated, or it may be the equivalent of a very weak and thus unconvincing handshake, as if he doesn't really mean it. But if he doesn't drink at all, you won't mind. In fact, since you know he doesn't drink, you won't initiate the toast at all.
Another example is the celebration of something important, like a wedding, or a wake. Unless you abstain from alcohol completely, it would be very rude to refuse to drink for the bride and groom (don't you wish them all the best?) or for the deceased (won't you honor his memory?). Again, it all stems from the ritual aspect of alcohol consumption: it "seals" and adds weight to so many things...
Third example, since I'm talking about wine(etc)-making cultures: it may be OK to refuse the beverage your host bought in the store, but what if he made it himself? Would you refuse to eat the food he cooked, too? Preposterous. You'd better have a very good reason.
And the most ubiquitous situation is when nothing special happens, except that you have a group of friends drinking. They all raise their glasses, and it's like saying "we're in this together". They push each other to drink, not because the goal is to get stone drunk, but because it's a "tactile" way of asserting again and again that they're equals, peers, friends. It won't be necessarily offensive to refuse a drink, but if there's not a solid reason (I'm driving, I'm on antibiotics, I'm a recovering alcoholic), pushing is very much expected.
Now, obviously, there's a difference between refusing the first glass and refusing the tenth. This is where it gets complicated, because for some cultures (or specific people) it's reasonable to stop drinking at point A, for others it's at point B, and for others only passing out will spare you the obligation. Is it limitless like that in Japan, at least in some occasions? Possibly. Another possibility is that the author of that book simply didn't drink enough to find out.
Disclaimer: Please note that the above are from an anthropological point of view. I'm not supporting any of it, I'm merely observing. If you don't want to drink, don't drink. And it should go without saying that these customs are a lot more pronounced in rural communities (especially where there's moonshine abundant), they get diluted when people move to a more urban environment, and become a rarity in the big city. Well, they can survive in a way, but most people don't take them too seriously any more.