That is not exactly an academic source and it's from someone living in Japan that doesn't read Japanese very well (check the comment section where they admit that themselves) so this is far from authoritative as a source.
I heard that after WWII the US occupation administered a national literacy test to see if Japanese people were as literate as their US counterparts, as it was becoming a serious idea to replace the existing writing system with the US alphabet. It was found that their literacy level was comparable so they didn't change anything so drastically.
Consider that learning to read kanji is much different from (easier than) learning to write them. There are a ton of contextual clues when reading, and furigana inserted by the publisher if the kanji would be hard to read for the target demographic. There is also the option of just substituting kana for hard-to-read kanji. Publishers and writers will obviously add furigana to any kanji that are hard to read as they have a monetary motivation to make their content as accessible as possible.
So you tend to pick up a lot of kanji based on these contextual clues and furigana over the years if you read anything, similar to how English speakers learn spellings of words when they read a word they've only "heard" before.
Writing is harder because when writing you will sometimes struggle to remember the correct kanji to use, or sometimes forget a small portion of the kanji. This is the why schools need to spend so much time teaching kanji as a subject of itself.