My theory is that in addition to wanting Tatum and the MEM pick, New Orleans wanted Danny to agree to the devil's bargain that the Lakers made: giving up control of the next 4-5 years of Celtics picks.
That demand would make an AD deal untenable, regardless of whatever AD's camp is saying.  If you KNOW AD is going to re-sign, then fine.  If there's a decent chance he may leave, let alone a GOOD chance, you can't let the Pelicans have control of your draft picks for several years following next season.  That is how you cripple your franchise for a decade.