You seem quite certain that the research is invalid and quite certain of your systemic racism hypothesis. I would invite you to find evidence for your hypothesis in the actual study results.

For your hypothesis that the study results are skewed by white privilege at least the following things would have to be true:
1. Neighboorhoods with more citizens from lower classes would need to be less green than neighboorhoods with less citizens from lower classes.
(At least where I live, in Amsterdam, that would presumably not be the case as the Bijlmer, one of the largest and poorest neighboorhoods is very probably the greenest one. As an aside, the amount of trees is sometimes seen as a problem for that neighboorhood due to the combination with high crime rates, as foilage provides cover for people with criminal motives, makes the area darker (less light getting through) and makes it feel less safe when combined with the sight of huge high-rise flats). This only adds to problems for the people living there and the stereotyping by those not living there :/).

2. The correlation between house prices and area income would need to be lower than expected but there would need to be a significant correlation between house prices and class (f.ex. credit score)

Contrary to your statement, I do think there's a large correlation between the first two, but I haven't checked with housing data for Toronto. For one, there's also the option to rent a house so the correlation between income and housing quality will be higher, as people with higher incomes can afford higher rent. If I read this report correctly, around 30% of Toronto apartments are rental ones http://www.trebhome.com/market_news/rental_reports/pdf/renta.... With rental homes, surely there's a large correlation between income and housing cost.
Secondly, while I do agree that income and class won't necessarily be correlated at the individual level, I would assume it evens out on the neighboorhood level. Neighboorhoods where people have good credit, income stability, good status, a good job, good medical contacts and access to good food, will surely have a higher average income. And actually, income does seem to matter when buying a house in Canada (http://globalnews.ca/news/985258/to-rent-or-to-buy-8-questio...)

So I am sympathetic to your argument that systemic racism makes it more likely that one lives in bad housing, but don't buy that this will explain the study's results. I do wish they would have worked with housing costs/rent.

You did make me investigate Toronto a bit. It has quite a lot of food deserts http://www.ehatlas.ca/built-environments/food-deserts, and apparently its child poverty rate is quite high. I'm often confounded by how cities and economies are built in that part of the world. In the Netherlands, cities are littered with supermarkets and the overall availability of bikes and scooters makes it even easier to get to one. Credit scores are much less of a thing here, too. Whether you can buy a house is based on income and income stability.

Btw, you do seem to be assuming the american(?) situation to some extent. Canada has universal health insurance and putting patients with deeper pockets in better rooms seems to be an odd explanation then, too.