There is no specific guideline, rule, or law that says any specific news organization has to be included or can't be excluded.
Logic would dictate that one would go with the press who has the largest reach in order to have the widest audience for your story but also, the market (ie people choosing) shows which outlets people prefer.
As stated above, choosing only friendly media to invite, while not against the rules, fosters the appearance of impropriety. It also gives the impression one can't handle the challenge of criticism.
That being said, it is a damned if you do, damned if you don't situation.
I remember when Obama started shutting out Fox for some briefings, our side went ballistic. Same situation, different station letters.