Restrict "updates available" messages with role-based permissions

The "updates available" messages appear to anyone with access to administrative pages. In some cases this generates confusion when it appears to people who have nothing to do with actual software maintenance on the site.

In other words, when my client, the client's employees, and my coworkers who help maintain the site see these, they either wig out and think they'll be hacked any second, or get annoyed because the message is bothering them, and then they all email me to say "there's something wrong with the site!"

It would be really helpful if these messages could be restricted to just the people who can actually do something about them - like the site's development team.