I don't know... in my post above, I was assuming they were, since typically achievements are associated with the player, not the character (in the original use of the term in video gaming, as in XBox achievements or Steam achievements).
But that may not be how they are implemented in ESO, in which case I was wrong about being able to get the ones you miss on an alt. Never thought to check in the beta, since I was assuming they were normal player-linked achievements
Edit: Hmm. Looking through the ESOHead list, I see that some achievements grant Veteran Points... which means they have to be per char. So not what I would consider a pure achievement system at all, as defined here: http://en.wikipedia.org/wiki/Achievement_%28video_gaming%29