I entered the same configuration, and I got the same results. Then I added another user "user2" with privs 0. But I didn't specify and commands to use.
I then logged in as user1 and used ping without entering "enable" and the ping went through just fine. But when I logged in as user2, I couldn't use ping. From what I can tell, when a user uses "enable", it gives them 15 priv. The priv level you set when making that user is the level of privilege they have _without_ using enable.
If you want to enforce these privs on these users, disable their use of the enable command.