The fact that you passed level 2 is irrelevant. Your actual ability is obviously well beyond level 2. By your reasoning, you could have taken level 4 and then made the claim that a level 4 ability is enough to read those books (which I was assuming you had read). I was careful to say in my most recent post that, "someone who is at (and not above) the requirements for level 2 (1000 kanji, 6000 word vocabulary) would have a fairly difficult time reading those books you have listed there."
As for me, I have passed the level 1 test, which I took last December, and I took and passed level 2 a year before that. I have had many failed attempts at reading Japanese books over the past 6 years but my first success was with book 7 of ﾂ青｢窶堙俄?堙?窶｢sﾂ幸窶堙遺?堙??堋ｫ窶堋ｲ窶堙? a series intended for elementary school children, which has furigana on most of the kanji. I began reading it shortly before taking the level 2 test, and finished about a month after the test. I looked up, and wrote down every word I didn't know (about 3000 words), and took the same approach for books 8-10.
After that, I started reading ﾆ椎?ﾆ停?愴丹 by 窶氾ｩ窶禿佛津ｵﾅｽi, but stoped halfway through to read ﾂ青｢ﾅ?E窶堙娯?吮??ﾂ心窶堙??､窶堙ｰ窶堋ｳ窶堋ｯ窶堙? which was considerably easier, before finishing ﾆ椎?ﾆ停?愴丹. I read about 150 pages of the first volume of ﾆ陳債ーﾆ筑ﾂ人窶堙娯?｢ﾂｨﾅ津ｪ, and recently finished reading 窶敘ｽﾅｽm窶堙戸?､窶堋ｵ窶堋ｽﾂ絶?敘ｽﾂｮ. After I finish book 11 of ﾂ青｢窶堙俄?堙?窶｢sﾂ幸窶堙遺?堙??堋ｫ窶堋ｲ窶堙 (which was recently published), I'm hoping to try to tackle ﾂ坂?倪?ｰﾃ??堙娯?｢iﾅ?i, if it's not too difficult.
So basically, I know from personal experience what it means, and what it doesn't mean to have level 2 ability because I was there a year ago. Even now, though I could probably read a book by 窶愿?窶彡ﾂ康窶｢v or ﾂ渉ｼ窶怒ﾂ青ｴ窶卍｣ without a tremendous amount of difficulty, it still wouldn't be easy, but maybe that will be different another year from now.