I don't think that it is clear that she is truly paralyzed. Certainly her family has repeatedly stated that she is "paralyzed below the hips." The Pelletier supporters repeat that statement, but really, there has been no medical documentation that Justina is in fact paralyzed. Perhaps she is in the wheelchair because she refuses to walk due to a psychological or behavioral problem.
Paralysis, like many things in this case, does not make sense. Even if she had a confirmed case of a Mitochondrial Disease, loss of function of both legs so quickly would be very unusual. Myopathy of that nature - if it happens at all - is a very gradual process - patients do not become wheelchair bound overnight the way Justina appeared to.
http://www.nlm.nih.gov/medlineplus/mplusdictionary.html
Midline Plus Medical Dictionary
Paralysis
Main Entry: pa·ral·y·sis
Pronunciation: \pə-ˈral-ə-səs\
Function: noun
Inflected Form(s): plural pa·ral·y·ses \-ˌsēz\
: complete or partial loss of function especially when involving the power of motion or of sensation in any part of the bodysee hemiplegia, paraplegia, paresis 1
It is not apparent from watching videos of Justina that she has a loss of function of her legs.