That's still not correct.

For HDMI in particular, there's no error correction at all on the video data (though there is on the audio and control data).

So if one bit gets flipped in the video data as it goes through the cable, you're going to see that wrong bit on screen. You'd have to have an insanely high bit error rate for your eyes to notice it, but it's there, and it gradually gets worse as the error rate increases.

What could flip a bit in a cable? Any number of things. EM interference from outside a badly shielded cable. EM crosstalk between conductors inside a badly designed cable. Signal reflections at badly designed connectors. Basically anything that can happen to any other cable, whether the signal that goes over it is considered to be analog or digital.

I assume the reason HDMI applies EC to the audio and control data is that errors in those channels are more noticeable to the user, whereas errors at reasonable rates in the video will mostly sneak by.

The HDMI spec at http://www.hdmi.org/download/HDMI_Spec_1.3_GM1.pdf is a great source of information about this.