I believe there is a check in place so even if you have it so regular users can "edit any post" it still won't allow it. Just kind of a safety measure in case it's accidentally clicked, since 99% of the time this isn't something anyone would want.
What you probably want to do is add another group and have everyone belong to that group as well and then you can assign the permission to that group.
Well, I did what you said, created a group, assigned corresponding permissions, but still the users (members of the newly created group) are not being able to edit other user's post
