As a side, my legal clinic represented the Haitian refugees who were children in asylum/visa hearings pro bono.
Then again, it's not like public-private partnerships (or project delivery methods in general) are brand new concepts. Governments have somehow managed to get roads and schools (infrastructure) built for a pretty long time. (Not without complaints of overruns and abuse: see any megaproject in the United States.) Though perhaps there is something to be said for the qualitative difference and value of human life that distinguishes a "race to the bottom" for building a road, compared to providing temporary shelter and food for actual human beings.
I agree that it's good that a government saves itself from getting into a "non-core" business so to speak. But I think that without strict oversight from government, refugee support services could turn into yet another field where shady business practices are the norm.
(There's also the surprising efficacy of vocally complaining in public. Do not underestimate a private firm's willingness to recuperate damages on its brand image.)
edit. addendum. These kind of firms have not that much of reason to care about their brand image when it comes to what regular people think about them: their only customers are some government officials (or in car park example, people who own the park space), not the general public.
In 2010, Norway spent on average $11,800 per year per refugee or asylum seeker in government operated centres. This amount covered lodging, health checks, nursery, and co-pay on dental and medical services. I don't know how much of that is the lodging, but it's nowhere near the whole amount.
The prices stated in the article adds up to $11,315 to $27,375 for just the lodging.
That doesn't necessarily mean that it is bad as a way to deal with rapid increases in the required capacity.