team A members are notified when team A becomes a member of another team

Some irc discussion indicates that there may be use cases where individual members might want to know about membership changes. Perhaps this should be an option when the invitation is accepted. If so, you definitely want to know how many people will be notified of the change.

Options might be to 1) only email direct team admins; 2) only email direct members (give count); 3) email all direct and indirect members (definitely give count)

Other possibility includes "hide the fact that you're doing this change from everybody?" check box.

You get the idea.

Are there any cases, other than accidents, where team members should not be notified that their team has become a member of another team?

If there are use cases for this, a checkbox would be a good idea (though I think it should be positive, i.e. "Notify all members of A that they're joining B", rather than negative, i.e. "Hide this change").

But the accident case wouldn't be fixed by any option. It could be fixed by giving the team admin 5 minutes to change their mind about the membership before the notification is sent out.

I find the use case for wanting to notify all team members kind of weak. We don't do that for mailing list subscribers when the subscriber list changes. Notifying bug subscribers that a bugs CC list has changed is one of the things Bugzilla does that I find appalling. We get this right in most cases; I don't see why we should spam in this instance.