Really? Are you signing her profile in before you sign yours out? Because every XBLA game I've ever been signed-out of has booted me back to the menu and defaulted to demo mode.
Decided to do a quick test for you. And got mixed results, strangely:
Cloning Clyde - Loaded in as me, signed out. Loaded in as her and had full functionality. I know I downloaded this way back on my first (or even second 360) and have had no reason to redownload it after changing license's over. Not even sure I've done the license migration thing on this 360, honestly, since it's my fourth one.
RoboBlitz - Another old game that I haven't turned on since I beat it years ago. Signed in as me, logged out, signed in as her and sure enough it's locked up and requires me to buy the full game. So either two things...
A) I properly migrated the license for Cloning Clyde some time ago for some truly bizarre reason. I have big doubts on this one.
B) Somehow games have their own restrictions as to if they let you do my "trick" of signing out as me and signing in as friends. Or does using a data transfer cable thing transfer licenses now? In which case perhaps I did properly transfer my license on a good number of games by redownloading in the past or something and then kept them alive by using data transfer cables?
So yeah, sorry, no real idea why it tends to work for me. I've done it a bunch of times with her as we sample my Arcade games often and I have around 130 or more now. It's hard for me to keep track of when I originally downloaded all of them and if I ever had to redownload or which of my 360s they were tied to. Also, I know there were a couple games where we had to do the sign in-sign out trick a couple times because it would mark her as a non-owner of the game. I believe Trials HD was one of them?
Thinking about it now there's also a good chance she was signed into a second controller on her profile and I signed out of mine but it still left her complete control of the main menu without the game rechecking proper ownership. That's another test I'll have to check for you.
Edit: Sure enough, went back to RoboBlitz with both of us signed into two different controllers and she was able to start a new game without a problem. Once inside the actual game I was able to sign out and her profile was still fine. I backed out to the main menu and it was the full game. Once I backed out to the title screen and went back in as her without me signed in it did it's recheck and then went back to the trial. So yeah, that's about as comprehensive as I can get with the checks. And since the original question was about DLC and he asked if it was because he was originally signed in then yes, that's why his friend was able to access it.