The problem you're running into is that a Group is basically an alias for a collection of email address and contact objects; not a standalone object, and not just a list of strings containing email addresses.
So when you reference group, you're actually referencing all member objects in it.
Similar to when you send to a group, it doesn't send it to the group's mail box (cause there's no such thing), instead, the server receives it and sends a copy to each recipient in the group.
So you're saying "Move all messages received from people in this group to X", yet you don't want it to move when you receive email from people in the group. Your 2 wishes directly conflict.
If you want to do a plain-text search and move based on what the group is named, instead of what it represents, then use the text-in-header rule you've suggested, and live with possible false positives.
Unfortunately one gotcha is that, unlike a regular "from" rule, this rule will be client-side only. Meaning it'll only work when your copy of Outlook (that has the rule) is being actively used.
Additionally, in Outlook 2013 (I believe that's the first version with it) they've added a new rule that's very similar to the message Headers rule, only it's "with specific words in the sender's address".
Either will work, but the second will help avoid the false positives you suggest (i.e.: it being filtered because the address is in the subject, etc.).
Best Answer
I have created a rule to match the country code.
This only half works though. Whenever a service with a name sends me an SMS they obviously goes through. Outlook clearly knows that it comes from the mobile phone, so there should be some more elegant way to do it.