I suppose you're counting the joyo kanji plus kana alphabets with diacritics. But the actual count of kanji is much higher, even if Japanese uses a relatively small number of characters for day-to-day writing.

Pretty much every native university student I met when I studied there, had passed the Kanji Kentei level 1 test. A certification of proficiency in around 6000 kanji.

Yeah nah imma call bullshit on that. Kentei 1 is notoriously difficult, only a few thousand people per year try it and the pass rate is single digits.