iMovie crops my photos!

Of course. Set the Ken Burns zoom to 1x (both start and end zoom). (It doesn't matter that Ken Burns is disabled as this only disables the motion.)

And you should be aware that a TV will crop the images, too. That's called overscan.

Follow Lennart's advice, but add one small step which will eliminate a pan, if there is one. (It sounds like there is one, which shows a border.)

After turning on the Ken Burns checkbox, click on the Start end of the Start/End thingy, pause for a moment, then drag the zoom slider a bit to the right, then drag it all the way to the left. Repeat for the End side of the Start/End thingy.

Now Ken Burns has been returned to its default settings with no pan and no zoom. Now the image won't get cropped.

Following Lennart and Karl, you might be able to make the adjustments to all your photos at the same time by selecting All or a subset of the photos.