A.J.
You are right! Nothing will work if they keep running circles around him. Cry it Out only works if they stick with it. Otherwise it's the Cry Until The Parents Give in And Now They're Even Worse Because They Cry Longer Method.
I think the naps going awry is a result of the whole nutty low sleep situation. Have a talk with them and explain that whatever they want to do, they have to be firm and calm and not budgee. Take it from my step sister with 12 kids, ANY CHILD, barring medical conditions, can sleep through the night alone in their beds securely and happily. If the parents want them to and they do it that way from the start which is easiest on the child. But anyway, now that things are awry:
He needs more food during the day. Nutritious, not sugary of course. He needs lots of exercise during the day and a little sun whenever possible. He must be TIRED and FULL at night. Then, he needs a good cozy bed that he likes. Then his parents need to LEAVE HIM ALONE after they put him to bed. Even the occasional comforting is causing him to cry until he gets it. Bringing him to bed is the WORST thing they can possibly do if they want him to sleep alone in his own.
Either they want to break this habit or they don't. If they do, they have to get through the crying until he has realized he can-and has to- sleep himself. They can do it gradually if they want it to take longer.
They shouldn't worry about him sleeping on the floor. That will pass, and it won't hurt him-at least he's asleep! They could put a comfy mat there! Also, don't worry about the naps right now. That will iron out when all is calm. At this point, if he misses a nap it may help him be tired at night.
They need to make a decision, stand firm, or give up, sleep with him, and stop all the drama. Good luck! Keep your input positive and praise how hard they're trying, but let them know his behavior is TOTALLY NORMAL as long as they are running in and out and doing stuff for him at night.