As far as I can see, the chords accompanying a song are just a subjective guide to a guitarist, reflecting the author of the tab site's opinion. You could have several tab sites for the same song with different chords. So I don't think the chords themselves are infringing anyone's copyright.

But if the site includes the lyrics of someone else's song, that is infringement of copyright. Many of them don't include the melody of the song, as it's assumed the reader will know that already (of course, publishing the melody on the site would also constitute copyright infringement).

What's to stop someone writing their own lyrics and publishing the chords for that? The lyrics could be any old nonsense, as long as they scan the same as the real lyrics (they wouldn't even have to rhyme).

For example, you could rewrite the lyrics to Bob Dylan's "Blowing in the Wind" as:

B*gg*r the sods who make up these laws
To stop us from publishing tabs
Any old crap words will do for the song
As long as it more or less scans
(etc.)

Hope you get the idea - would it be a way round the law?