The possession of the money is treated as probable cause. The police are not tasked with finding the ultimate truth of things, just acting on probable cause.
So you’re on the road with $10,000 in cash. The police find out. You tell them the true reason. They write it down, then seize the money because it was suspicious to you to carry $10,000 in cash.
Then, of course, you can go petition to get the money back. At which time, you have to prove by a preponderance of evidence (the same bar as if you were suing them for damages) to get the money back.