--you're right.

People with CIDP are unlikely to have that kind of full-body inability to feel pain. (There are such conditions, but they are generally hereditary, not acquired, and rarer than CIDP, or B12 deficiency.)

People with CIDP are much more likely to have dysesthetic sensations, parastheses, not infrequently painful, and numbness/loss of sensation, but this is generally "mild" and far from total. In fact, CIDP, like Guillain Barre, tends to present with motor symptoms greater than sensory.

I did not see the House show, but it seems to me if they were tossing around the CIDP term the more acccurate presentation should have included motor weakness and lack of coordination with "weird" sensory sensations.