Those are some interesting questions @Miho Hatanaka.
I have also had some foreign friends tell me about the difficulty of renting an apartment in Tokyo. In some cases the reasoning makes sense to me, as a property owner myself: it's not a smart business practice to rent to a tenant who is only in the country under a short-term status, who does not have proof of sufficient employment, who does not have a guarantor (we'd often just call them a co-signer in the US), and with whom the landlord cannot communicate (if the tenant doesn't speak good Japanese). In other cases, I think landlords are being close-minded, as you say.
From personal experience, I was definitely turned away from units the moment the real estate agent told the landlord I was foreign. There's no rule against refusing to rent to foreign persons. It was frustrating, but I tried not to let it bother me, and I was always able to find something nice. The same thing as if someone said they wouldn't rent to me because I'm obnoxious or I smell. It's not nice, but it's kind of true...
I think it's a different story when you talking about sales, however. Not sure about the woman in Saitama, but my guess is there's more to the story than her just being Chinese. Some could be cultural. To use a common example, bargaining/haggling is not common in Japan. It's the norm (I hear) in China. Suppose the Chinese buyer was constantly haggling to lower the price for this and that? It would certainly turn off a seller. Still, Japan has no rules against foreigners owning real property, unlike some other countries, particularly in south east Asia. The difficulty that most foreign buyer's have, I think, is with financing. Most Japanese lenders won't lend to foreigners who aren't long-term residents or permanent residents. That's different from the US. A non-US person can still get a loan for investment property in the US. Of course, the terms are tighter - for example, 50% down and 2% higher interest rate. But it's possible. My understanding is that non-Japanese buyers who aren't long term residents have only one real choice: an all-cash purchase. That may work for some wealthy non-Japanese people (for example, it's popular among affluent Chinese), but it's not a strategy that makes sense for most. Most Americans would be much better off to invest in the US with a loan than to invest in Japan all-cash. To me, this is more the investment background than the opinions of individuals. I'm willing to bet most Japanese sellers would be fine to sell to foreigners, that it wouldn't really matter to them. Plus, property rights in Japan are strong, and there is very little corruption. So foreign buyers can be very confident of what they are getting. It's a pretty safe bet.
I'm going to ping @Kiley N. and ask his thoughts.
One last thought: It's not a purely Japanese problem. I'm not sure how things are in Portland, but I'm pretty sure there's some discrimination based on national origin in a lot of places in the US too. Granted, there can be better chances for remedy/compensation here, I think.