No, it really wouldn't depend on the type of interference. Any interference should upset a nationalist because any interference from a foreign nation, no matter how small, compromises our sovereignty.
It's like someone saying they believe in completely monogamous marriages but they're okay with a little cheating.
The 2 positions shouldn't co-exist. If someone is okay with even a little foreign power interference then I say that their nationalist bonafides are in question. They can use the information and still be up in arms about how they got it.
And of course it should be more enraging than a billion media outlets if the media outlets are run by members of your nation. Nationalists should put their nation and their nation's members above foreign nations. Claiming that a foreign power is less concerning than a corporation run by legal citizens just means that "nationalism" isn't what drives the value system.
But maybe we're using different definitions of nationalist?