what does "honest to a fault" mean?

here is a selection of what the interwebs think about it's meaning:

http://www.dictionarist.com/honest+to+a+fault

http://wiki.answers.com/Q/What_does_Honest_to_a_fault_mean

just for fun:

http://www.lyricsmode.com/lyrics/a/at_the_drive_in/honest_to_a_fault.html