This insurance issue has always been a little fuzzy, but after talking to Marianne and my insurance carrier, my understanding is different than yours.
In addition to covering the contents and personal injury, you need to cover reconstruction of the interior of the apartment. The coop does have insurance, but it only covers up to the drywall. So, if you have a fire in your apartment, you would be responsible for rebuilding the interior (e.g. bathroom, kitchen, floors, ceilings, closets, etc.).

So, you don't need to insure the entire value of the apartment but only what it will cost to rebuild out the interior.

Of course, if your apartment is damaged by water/fire originating from another apt., the coop's or another shareholder's policy should cover your dammage.