well,the "just cause" of it would to make sure you're there legally,which is what I was trying to imply. I honestly see no harm in that.
That is not "just cause". The same thing holds for police inspecting your car or home. If there is not reason for them to suspect something is amiss (and the key here is "reason"), then they have no legal right, in the USA or Japan, to ask for your ID. Perhaps you should look at what Debito Arudou has to say about being stopped by the police for no "just cause", only to verify your passport. http://www.debito.org/instantcheckpoints2.html

I'm sure they have stopped Japanese citizens before, and I hope you don't argue against that.
Yes, they have stopped Japanese citizens before for bike registration. People have reported, however, that after they (foreigners) are stopped, then they ask the cops if Japanese are being stopped too, the cops say yes, but totally ignore any passing Japanese at that time on bikes. So, it's a case by case thing, and if you are stopped and are the only one who is stopped, it is suspiciously like discrimination, don't you agree?

A privately owned business doesn't have the right to turn anyone they think won't/can't make the payments away? That's the arguement I'm sure they use, or something similar, and it'll probably hold.
Stop moving the goalposts. You originally said they "have the right to turn you away for any reason". The reason you just cited is totally valid. You think they turn down foreigners for only valid reasons? Nope. Lots of apartments turn away foreigners for the most ludicrous of reasons.

Examples:
We stink (or our food stinks).
We don't know how to use tatami floors.
We won't be able to understand enough people.