You absolutely could put in disks upside down.

I recall doing this on my BBC micro with 5.25" disks. In fact, some disks were deliberately designed for this, and had a 'notch' (which you would cover with some tape to make read-only) on both the left and right, so you could set the read-only state for each side individually.

The version of Elite that I played had the standard version on one side, and a version for the "BBC Master" (which had an extra 64KiB RAM) which had more colours than the standard version, on the other.