I've no idea, it's not because your cart has been updated because i've update mine multiple times.
I know the DSi update works on both the DSi and DSL, but i've never tried the DSL update on a DSi. Normally you want to use the DSi update on either console, because it has a lower brick rate because as you've discovered it doesn't ask you to eject the cart. What happens when people run the DSL update is they flash their cart and at the end accidently press start again. It starts flashing their cart again, the user panics and powers off mid flash. They then end up with a bricked cart, this may have been what your friends did.
All I can suggest is you borrow a DSL and use that, do the same cart swapping as above.
You don't need to swap SD cards or have the update on the SD cards. Once you've run the DSL update, it's in the DSL's memory hence you can then swap the flash carts over.