Twilight - playable at any point?

[Shapeshifter]

Another Twilight-question.

Card Erratum: Add "This card may be played at any time during any player's turn."
Can target a card that has not yet resolved.
Can be played as a resource during your opponent's turn.

The situation is as follows:

Doors of Night is in play - m/h-phase starts - cards are being drawn - player draws his first of two possible cards for the company's new site - it`s a Twilight - this copy of Twilight he plays immediatly to discard Doors - afterwards player draws the second card.

I know that usually cards may not be played while cards are being drawn. Does Twilight override this ruling?

[Bandobras Took]

It can't interrupt card draw so far as I know. It can be the first action after card draw, but

Players drawing cards when a new site is revealed is synonymous with the resolution of the new site being revealed. It happens immediately, not in the following chain of effects.

You can't declare new actions when a chain of effects is resolving. You have to wait for card draw to finish because it's part of the resolution of the site being revealed.