I don't think there is any way we could possibly know if INFJ's are rare or not. It would be impossible to get an accurate count on something like this. And that goes for any type. So to claim rarity is a bit ridiculous.
I do agree that there any many people that claim to be INFJ but are probably not (this doesn't bother me, just an observation). And I couldn't agree more with you about needing to be honest with yourself when taking these tests. People are cheating themselves if they are only picking answers that they know will produce a certain result. That's silly. But then again, there are a lot of people that would like to be viewed a certain way, so they answer the questions according to how they wish they were. Which goes back to being honest with yourself.
I took the test a couple of months ago and took my time going through every question. I went through situations in my head, how I reacted to them, how I process things, etc. the whole point was to make sure every question was answered with 100% accuracy. I then copied the results. Then I went back and did it again with my husband present. He answered the questions on how he saw me and the way I process things, etc. At the end of it all, the results were the same. I think the confusion I lies in the fact that my other functions are very highly developed. This could also be an issue others may be having.
And I don't believe that if a person doubts their INFJness, then they are not an INFJ. There could be a number of reasons for the confusion.
Anyhow, my results were INTJ.
Oh, and for the record, Winnie the Pooh is not INFJ or any other type for that matter. He's a cartoon.