Once again, the ambiguity of 'attack' rears it's ugly head. I wish WotC would get a clue and fix all ambiguous references to 'attack,' changing them, explicity to 'attack power' or 'attack roll.'
For instance, in the Wording of Tactical Pressence, the use of the singular strongly implies that it should be 'attack power,' because you can spend an action point to make multiple attack rolls, but only to use one attack power.
I guess it's still ambiguous how AEs work. AEs make multiple attack rolls, not multiple attacks (for instance, they all use the same damage roll), and the FAQ ruling still unhelpfully uses the ambiguous 'attack' (though, I guess it has to, since it's not supposed to issue errata, just clarify).
Anyway, as a DM I wouldn't use it (wouldn't be the first house rule I'd prefer), and, as a player, it makes the tactical presence much less desireable - unless the party just happens to lack any serious multi-attack capability (in which case, maybe they need me to play a Wizard or Devoted Cleric more than a Warlord, anyway).
Paranoid Conspiracy Theory: This is clearly a recent FAQ entry on a relatively old rule (it's after the new Magic Missle entry). It could be part of the push to make 4e Essentials-compatible. The new basic-attack-spamming/enhancing martial classes potentially make the Warlord, particularly the tactical warlord, a bit more powerful, this could be way of compensating for that boost without nerfing or further complicating basic attacks, themselves. It also makes the Warlord work better with other martial classes than with casters, emphasizing the difference between martial and the other sources.