I am almost certain that @David Gotsill was turned down by landlords due to either obnoxiousness or smell.
Seriously though, from the Japanese side I have heard stories of the difficulties in renting to foreigners as opposed to renting to Japanese. To be fair, almost any generalization of a population is sure to be inaccurate in some or even most instances. In the case of Japan, homogeneity (whether real or perceived) lends itself to comparison with other populations as a whole but does not necessarily reflect the actual reality of each situation. ESID (Every Situation Is Different), as they say. Also this comparison very much occurs both ways.
I would second @David Gotsill 's final thought that it is highly likely that the same, or arguably worse, generalizations occur in the US as well. Were it allowable to screen tenants based on nationality, I imagine the US tenant experience would be dramatically different.
A big part of investing (or living) in a particular country is one's level of familiarity and comfort with that particular area's way of doing things. For these inter-cultural agreements to exist harmoniously it is generally not a requirement that either side needs to acquiesce to the other per se, but rather that shared respect for a minimal level of common laws/truths/norms are upheld by both parties; the clearer the better.
My personal experience renting in Japan was fine and I was never turned down for a place but I also was fortunate enough to have a connection to either the landlord or the current tenant that I was replacing at the time. One of my landlords actually enjoyed me stopping by each month to chat and practice her English. I purposely chose manual payments over automatic bank debit because of that. I suppose this familiarity, and having a trusted individual vouch for me, is what may have made the difference. Another example giving credence to the BP podcast slogan that your network is your net worth.
I think the overall point is that there will be varying perceptions of any single event, whether positive or negative, by all involved and it is the generalization of those perceptions that often results in misaligned expectations. I wouldn't say that the Japanese as a whole are close-minded to outsiders, but I would also admit that it can and does exist. ESID.