That means that each single key may correspond roughly to 2256 / 2160 = 296 addresses, right?
Roughly each address can be accessible through the set of 296 keys.
Your first statement is the wrong way round, but your second statement is correct. There are 296* private keys per address if they are all distributed evenly.
*Actually slightly less, since there are slightly less than 2256 total private keys, but the difference is minuscule.
My bad, mine first assertion is totally reversing black and white, perhaps I have been deeply drunk when I wrote that.
What I actually meant is expressed by the second one. And agree, all that is correct only at even distribution.