I was just recently mulling this same question over about myself. When taking the test, I'm very close to F but still a J... just slightly.
I found that this page helped sort out a lot for me -
INFJ or INTJ?
It's not that we INTJs find somebody in distress and stop and think "Hmm should I help them? What logical way can I justify helping this person?". From reading some posts from INTJs I'm sure there are probably some people that honestly wouldn't care one way or the other, a big part really depends on the person and the situation. It's very specified, and it takes more and more experiences to be able to relate them to each other. It isn't that INTJs dont feel or dont care, they just aren't going to let emotions make their decisions for them. They might come to the exact same conclusion as an INFJ, but had different methods of arriving there. For me... I have emotions, I try to understand the emotions, and try to figure out why X emotion happened instead of Y in a given situation. For me it isn't that if I can't find a justification then the emotion isn't valid or important (but it does become incredibly frustrating if I can't figure it out). I can't just let emotions exist for the sake of existing.
For example... a few days ago I broke up with my boyfriend of a year and a half. I've been having feelings of anxiety and confusion, but it took me a while to understand WHY I was having these emotions. I didn't want to just break up with him for nothing. It took me months of 'waiting it out' to make sure I was doing the right things and to make sure I couldn't salvage the relationship first. I loosely applied the scientific method to finally come the conclusion that I needed to break up with my boyfriend and that we weren't right for each other, even if he is a great guy and we get along great. If it wasn't for those emotions nagging at me, I'd be stuck in an unfulfilling relationship for a very long time.... but I had to understand those emotions, categorize them, and justify them before making any decisions based on them alone. It is this decision making process and 'justification' that makes it possible for me to leave the relationship feeling a little nostalgic, but not an emotional mess. It's not that I don't care about him anymore, or that I didn't constantly worry about which way to break up with him for fear of hurting him.... but I can accept my feelings for what they are, and also feel good knowing that I did what was right.
I LOVE analyzing people's emotions and feelings, figuring out why they exist - it's irrational in my mind to assume that feelings are trivial. From an evolutionary standpoint, we evolved to have them to help us survive, and they help us survive in social interactions still. It would be unwise to completely shut emotions out and pretend they are useless. I've noticed that a lot of INTJs use their "label" as an excuse to be cold and rude. The same way that I don't think it's right for an INFP to use their label as an exuse to be an emotionally abusive and volatile train wreck, I think it's weird that people accept that it's okay for an INTJ to be an ass to somebody just because they don't immediately grasp that their actions and words can be hurtful.
If all INTJs were as emotionless and cold as many of them let on to be, or as a lot of people seem to think they are, you would probably find the INTJ to be an actual disability and not just a personality type. They wouldn't be able to function in normal society, because they wouldn't be able to interpret their bosses wishes or ever be truly involved in a romantic relationship. I reject the extremes. Extremes are irrational.
I find myself relating to people very easily. I pick up on social cues and I empathize with characters in books (or from stories of friends) to an extent that I feel physically heavy from taking on the emotions. Do I still find myself to be an INTJ? Absolutely, because of how I interact with these emotions and how I let them effect me. I do sympathize with the 'protector' image, and I stand up for those who are getting picked on... but only if it isn't justified for them to be getting picked on/punished. I wont stand up for somebody if I feel they deserve it (it's the justice vs mercy argument). For most people that I don't know well, my sympathies are conditonal. If I know the person well and they mean a lot to me, it becomes more unconditional, and mercy begins to outway justice - which is still rational to me. It makes sense to protect the ones you care for, as an INTJ, I just don't extend this feeling toward every person alive.
(huge post, really sorry... got caught up in dispelling the negatives revolving around the diea of an INTJ)