Alright, I bought Sega Bass Fishing on my own console. It plays fine on there, no problems. However, when I visit my parents I use their 360, using my memory card to sign in to my account (the same account which purchased the game). In this situation, the game behaves oddly:
When I start the game, it asks me if I want to use the hard drive or memory card (normal behavior for a purchased game). However, the main menu is that of the trial game - I can select "Play trial game" in which case it acts like the trial game. If I go to the "Unlock Game" option and hit A to select it, the game makes the selection sound but does nothing else (it does not take me to another screen nor allow me to purchase the game again). It's perpetually stuck in trial mode.
From the 360 dashboard, the 360 recognizes it as the full game. I have tried redownloading it multiple times to no avail. I tried to contact Sega customer support and wrote a detailed bug report only to be told that it was a "feature" to prevent unauthorized use and I was refused further support.
I'm guessing this is a bug on Sega's end, but it's seriously lame. They shouldn't be able to sell their game on Xbox live if it has a bug that literally prevents me from playing the game.