Can I get in trouble if, at customs, the police finds media files that I can't prove are mine?

I would not worry about this. I have never seen any officer opening a laptop and looking at the contents. What they did at one point some years ago was asking people to switch them on to make sure it's not a disguised bomb but actually a working laptop.

Custom officers are more worried about fake goods when people come from certain Asian countries, and duties payable when importing goods.

So on your PC or phone memory, you most likely will not have any issues. If you carry ripped DVDs around you that are marked with movie titles handwritten on them, you will be in trouble for sure.

Naming your files "Xmas Ski Videos" will also be better than the actual film title. Be aware that locking your windows with a password or other methods of locking them away does not necessarily help since there are countries (like the UK) where keeping an encryption key or password secret from the police is already a criminal offense.

Obscuring data is better than locking it away. Truecrypt can do that, too. One other option that you have is to simply create a partition, putting your files in there and dismounting the partition.

As a general guideline for passing customs: The more nervous you are, the easier they spot that and pull you out. Keep your hands in your pockets or hold your bags, do not fidget around and rather look at them as if you are inspecting their uniform. People who try to look away, cover their face or act generally nervously will be pulled out much more often for routine controls.