Whether or not spending actually influences elections, most politicians certainly believe it does. Or they wouldn't spend so much effort on fundraising, and wouldn't bother with the stupid ads. They clearly believe it works. Surely they know. Modern campaigns track this stuff religiously with polls, statisticians, and A/B tests. And this belief corrupts our democracy.

One example doesn't disprove it anyway. Clinton lost. But she might have lost even worse without the spending. It's impossible to say the spending had no effect. As the election was pretty close in many states, even small effects can make a world of difference.