Oh, absolutely, x2. It's also a clearly Realist statement. It doesn't matter if it's poor white people, poor black people, poor brown people, and so forth, moving from their shithole to a nice town, the issue is, once the nice town starts getting too many poorer people, the town starts becoming a shithole just like the town the poor people left. When you have a lower middle-class to middle-class town of whites, and poorer blacks (lets say blacks, as is common theme in the Chicago scheme of things) start moving there because they want out of their shithole (and no blame on them there, who wants to live in a shithole?), it triggers two things: 1.) white flight - they're getting the F out not because they now have a black living next door (most of them don't), but because they're getting out before the town goes to shit (and, historically, it does, so in the end, they're right), and 2.) the word gets out from those moving in that Yeah we moved to <x>, it's so nice there!, and, more come.
When it's almost all white communities with blacks moving in, and the town goes to shit, it's not hard at all for whites to conclude that when blacks start moving in, things are eventually going to go bad (that them doing a white flight adds to the problem doesn't cross their minds)...it's easier to see due to skin color. If it was poor whites moving in the effect would be almost as bad, however, because of same skin color it's harder for original town inhabitants to determine, so less/delayed 'white flight'. We can actually see that in towns on the border of the now shithole towns. There is still a really good % of white there but it's not middle-class whites only now, we've got the whites are indoctrinated in shithole living. And surprise surprise, the towns are slowly becoming shitholes.
The long and short is this: If you're in a nice town, you want to make sure you keep the shithole element out. You want people with the same core values, and application of those values (because wanting a nice looking yard and actually putting forth the effort to have that nice looking yard are two completely different things), to move/stay in your town, and you want to keep those that have lessor (relative to you in the town) values out. I really can't blame the owner in your example, why take the chance of adding to white flight and that your parents wouldn't share the values and application of those values? Sucks for you and your family but for those living there, makes perfect sense.