Oh my god how can you conclude like wrong all the way.
No one is suggesting your parents didn't feel they needed to apply for asylum, what is being noted is that the government determined that their claim for asylum wasn't substantiated. That unfortunately means it wasn't a genuine claim for asylum.
Now, while your parents may respect the process and may intend to respect the terms of a supervisa, it's unfortunately exceedingly unlikely they'll get a supervisa because they claimed asylum and failed in the claim.