Not sure if this aspect of the problem has been mentioned yet or not but here goes: I bought TTK digital download on my account and had the same problem - my kids couldn't play using their profiles (Xbox 360).
We just bought a new, second console for the house and I needed to buy the game for that console anyway so I bought the disc copy of the TTK Legendary edition. I installed the game on the new console using one of my boys' accounts and hoped for the best. It turns out that TTK is playable from all of our profiles on the new console.
So I'm thinking that the problem of the digital copy not being playable by all sub accounts must be a glitch because how could Bungie make the TTK playable for all accounts for people who bought the disc copy but not for those that bought the digital copy.
Hope that it is a glitch and that Bungie will fix it soon!
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Same. We just want an answer too about this issue but nothing.