In a whole lot of industries, there is a sort of "soft cartel" anyhow. I mean, I do hope they bust this app and the landlords using it, but. . .
In most industries, there is at the minimum, all participants tracking the pricing of "the market" and raising prices accordingly.
If they were only using public pricing information there would be little question as to the legality. There might be a small crack in the door with regard to keeping units off the market when the software believes there to be an oversupply, but it's a hard argument to make.
By making use of internal client-specific data as to actual rents being charged, though, there is a strong argument that illegal collusion is occurring.
This has already been hashed out with regard to airlines. They tried using their GDSes in a similar way and got spanked for it decades ago. What they do now is use public pricing signals. It's still, in some sense, collusion, but it's not illegal because they do it in public and aren't making backroom agreements with each other. Everybody who cares to look can see exactly what they're doing.
One airline thinks prices should go up, so they increase their published fares. If the rest of the market agrees, they quickly follow suit. If nobody else does, the original airline reverts the change, usually within a few minutes. It's the normal means of price discovery in a free market, just sped up.