I just did some testing, but with or without opacity mask won't make a difference. In a test setup I had no haze on the plane, and a crop test of the same file just now, didn't have it either, strange.
Interesting; when using a (displacable) plane, it's not working properly, because the transparent part is subdivided less (like water, so I'd have to set subdiv levels to 1), and with a card it's fine. Probably they are calculated differently.