Supposedly some 80,000 people, mostly Haitians, have attempted to apply for an appointment with a regularization/naturalization official and only around 300 people out of those 80,000 actually qualify. Doesn't sound like preferential treatment to me. Most people that haven't been able to qualify the first step is due to lack of proper identity documents and most of them are Haitians.
There is also an issue with Haitians getting their identity papers from the Haitian government officials at the Haitian embassy and consulates, so they are not getting preferential treatment from that side either. Much of this part of the problem is the cost the Haitian government is charging, which is too high for many undocumented Haitians. There is another problem that is not being talked about and that is the time it takes for the Haitian government to hand the documents after a Haitian asks for them and pays. I few weeks ago I read something about this and if I remember correctly it said that it could take up to six months just to hand the papers to whomever asks for one.
The regularization/naturalization plan ends next year and whomever is not at least in the process, even if later it turns out they are not qualified, will be in a tight situation.