I'm not advocating that in the real world, the bigger story is about who's releasing the info, rather than the info itself. However, there are issues when not taking both into account.
In specific terms this is equivalent to saying "Russians showed us proof of Dem corruption" and the response by the media is "well imagine that there's worse GOP corruption that they haven't leaked"
There are military generals who have served under multiple administrations. When they decide to go to the media and talk about some negative story about one administration, by your reasoning, it means they're telling a selective truth - unless you choose to believe that they only ever had differences with one administration.
There are whistleblowers from the State Department, DOJ, EPA and all kinds of bureaucracies. Are their stories ever met with this standard - i.e. "you're saying the W. Bush administration did this unethical thing, but you aren't telling us what the Clinton administration did". Was there ever a "I'm sorry Mr Deepthroat you may be right about Nixon but you have not told me what LBJ did, and for all we know, that may be worse"
You're absolutely right, and it is frustrating to no end.