First a self-correction;
I wrote the above after experimenting with a Shimano 7 speed cassette, which does have three pins/rivets to hold the main cluster of cogs together.
When I came to repeat the process on the live Sram 7 speed cassette, I discovered it has two pins and one minute 1mm Allen screw holding the cluster together (the type mentioned by a previous poster), making disassembly of the cogs easier.
For those who like a happy-ending: This is not for you
When I attempted to slide the cassette on with its cogs flipped, I found Mr. Cheese's comment still holds valid, and the cassette will not slide onto the freehub.
Why not?
Because Mr. Shimano-san (and copied by Mr. Sram) pre-empted this particular codge by manufacturing one of the splines narrower than the rest, and its adjacent spline wider than the others. So if you try to flip the cogs, as I have done, the cassette has the narrow spline to the right of the widest spline, but the freehub still has the narrow spline to the left of the widest spline. Result; Like shy Giant Pandas: They just won't mate.
Conclusion:
On modern Sram and Shimano 7 speed cassettes (and 8,9,10 speed too) it is not possible to flip any cog.
You +have to+ either replace the worn cogs, or buy a whole new cassette.
Congratulations to Mr. Cheese, please send an SAE to claim your prize of a coveted day-glo Turbo sticker.