I contacted MPEG-LA and asked for a license. They quickly sent me one (I asked for MPEG-2, MPEG-4 and H.264.) After the licenses arrived I signed and returned them. They later contacted me because I was an end-user and would not license to me. (Email copied below.)
I'm glad that I tried. If they're now saying that end users can be held responsible, I will keep these signed licenses (and the entire email chain) in my records. In the event that I am sued my plan is to pull these out and say, "look -- I tried to get licensed -- they refused" and go on about how it doesn't seem quite right to refuse to license to me while also suing me for not being licensed. Anyway, here's the relevant snippet from the email.
"Although our Licenses do not directly provide coverage for an end user and anyone in the product chain may be held responsible for an unlicensed product, a royalty paid for an end product by the end product supplier would render the product licensed in the hands of the end user. Therefore, the end user would not normally pay a royalty to MPEG LA for using such a product, but where a royalty has not been paid, such product is unlicensed.
In this case, as you appear to be the end user, we suggest that you choose a player from a licensed supplier. In that regard, we maintain lists of Licensees in Good Standing to each of our Licenses in the corresponding sections of our website http://www.mpegla.com.
Finally, please note that since you will not benefit from coverage under the Licenses, we will not execute the signed Licenses that you have returned to us."