(a) They are involved in that bill, or
(b) They belong to the group which that bill is a part of.
There are no special "user permissons" based on who originally added the expense, or who created the group. We think it's important that Splitwise act like a wiki, where anyone involved can correct mistakes and fix problems. Imagine if someone added an incorrect bill to your account, and you had no way to ever remove it!
If you wish to receive alerts about changes to your accounts, you can turn on notifications to receive an email any time an expense is created, updated, or deleted. You can also see a record of recent activity in your accounts by clicking the flag icon at the top of the screen on our website. (The flag turns orange whenever there have been changes in your account since your last visit.) We hope these notifications help to keep you informed about what's happening on Splitwise.
Alternately, you can create a group without entering email addresses for any other group members. This allows you to keep track of group debts privately, and then tell your fellow group members their balances later.