PBS is free over-the-air in the U.S., so the only thing PBS checks for is whether your internet address is indeed in the U.S.

Fortunately, there's an app for that! I use
https://www.tunnelbear.com/
TunnelBear, a free utility which connects your UK internet to a US server. Magically, the US server looks like the origin of the streaming request. (You can mimic connections to servers all over the world!)

Test it first:
Once Tunnelbear is running, visit here for a brief animation:
http://www.pbs.org/pov/schoolsout/video/storycorps-shorts-schools-out/
If that works, then you're in!

Sometime between 22 and 30 October, visit
http://www.pbs.org/wnet/gperf/episodes/hamiltons-america/

episodes are kept for a week minimum, although some stay up for years.

(I used these tools to watch Sherlock premieres, until BBC required proof of paid licence).