Well, apparently after me losing around 100k to bribing Rainbow of Victory Jack Frosts, I find out it's entirely possible to get those special demons with the weird titles above their names. The catch? They lose the title after being sent to your comp. They show up no different then a normal demon on screen, but keep all their special skills, stats, and whatnot. If I have to guess, as long as the game tells you that you can't capture a demon, it's up for grabs.
For some reason, the titles just vanish on these demons. Not sure if it's a bug or not, but others like Lost, Lucky, Unseasoned, Wounded still do appear. And of course, you can't capture any huge Incantation or boss demons.
Kissy Pixie of the dude who showed me his Rainbow Jack Frost with Frost Punch. Take note of how much it rapes his MAG cost. D : Thing costs more than my Archangel!
Now I really want my Rainbow Jack Frost ...okay, sure. It's not very practical to use. It's a stupid Rainbow Jack Frost, hee-ho. But come on. SNOWMAN PUNCH.