No, it's a campaign expenditure because it was
intended to influence the election, i.e. prevent a woman from telling about an adulterous affair with Trump while his wife was home with a newborn that any rational person would understand might lose him some votes.
The law is at
52 USC 30101(8)(A) :
And also 9(A):
And your definition would essentially obliterate all campaign finance laws, limits, required disclosures and more. The statutory limit is $x. Fatcat donor makes the statutory limit, then out of his own pocket pays campaign staff, planes, advertisements, $10 million, whatever, but because it's not paid by the "campaign" it's not a "campaign expense." No limits, no disclosure! Surely you see that's an impossible interpretation of the law.