The idea that the J/P switch doesn't work is pretty standard. But it gets complicated. First of all, I've long noticed that among MBTI enthusiasts, there's a tendency for people to fall into two camps regarding how they understand the functions with the consequence that one person may consider himself INFP whereas another person would consider that person INFJ.
What's probably the most frustrating, from a Socionics point of view, is when someone with an MBTI background clearly understands his/her type in terms of functions, and is actually certain about the functions involved, and yet has a result that doesn't seem to make sense based on Socionics theory...for example, someone who is absolutely sure that he/she is dominant introverted intuition with extraverted feeling, say, but also describes him/herself in ways that sound incompatible with Socionics IEI.
Differing definitions and theoretical constructs clearly play a role. But in addition, the person may be mistaken about I/E and actually be an EIE.
Also, I've seen some interesting cases where historical typings were done that have the functions similar to Socionist's typings, but the S/N and T/F flipped, so that what one might view as the valued functions come out the same.
For example, I've seen typings of Abraham Lincoln and some others as MBTI ISTJ, whereas around here they're seen as EII.
Another thing that may happen is that one has different subtypes, so that generally a typical Socionics understanding of types and temperaments would be most compatible with the accepting subtype, whereas the J/P switch works more with the producing subtype. Or, we might not call this "accepting" and "producing" subtypes exactly, but in any case, two subtypes corresponding roughly to "accepting" and "producing." Another related idea is to think of the so-called "+" and "-" dimension flipping between two subtypes.