No, on the old ATV you had a category called "movies" (for example), and one of the subcategories was your movies, while other subcategories represented the apple store and so forth. All movies, whether they were your own or possible rentals or purchases, were in one column, all tv shows in another, all music in a third, and so forth. At some point, Apple mercifully made the default under movies my movies rather than the apple store.
On the new ATV, movies to rent are in one category, as are TV shows to rent, and so forth. If you want to buy, you have to go to your computer. The default is movies to rent; you then have to navigate to computers, choose the computer you want to link to, then choose music, movies, tv, or podcasts, and then choose what you want. The new system involves a lot more clicking to get to your own stuff.
The only way around this is to use the remote app, which also happens to be the best choice if you have a large collection, as I do.