I think the scheduling is all about TV. The broadcaster wanted games to be played on Tuesdays, Thursdays and Sundays.
Usually you would want a series to start on Tuesday so the biggest rest (from Thursday to Sunday) comes when teams have to travel from the East to the West or viceversa.
But due to how the series in earlier stages went this year, they couldn't get to start the Finals on June 4th and waiting until June 11th to start was not going to cut it.
I don't believe this was intended against San Antonio either, since the June 6th start was scheduled when the Conference Finals were ongoing and at that time people still expected Memphis to have a chance.