That is what I thought at first based on the results I was getting, but then I was confused because intuitively it made sense for it to be the second player palette, because like the player the HUD is constant through out out the game (rather than having to always have the same 4th screen tile palette devoted to just the HUD). One of our 4 screen palettes is a lot to take up just for the HUD, but I understand that I am sure there is a good reason for this. I'll have to plan my palettes better if I only have 3 and not 4 to vary between screens.
Also I was second guessing it based on the video. You can see that when Joe previews the HUD it is using the last screen tile palette. But then in game it is different colour (black, white, red hearts as opposed to purple, blue sword handle).
UPDATE:
In the video, the hearts and HUD and everything you saw when previewing it looked like it matched the 4th subpalette, with the hearts taking on a kind of purple colour. This appears to be just the default palettes that exists before you change stuff. I opened a new file just to be sure, and the default colour there is purple and it looks the same as what I have screen capped here. In game, the hearts look very much red. Then, when Joe shows the colours being drawn in the HUD using the debug menu in the emulator (At 1:15:20 in the adventure video), he gestures toward the second palette in the bottom row, which is the second player palette, but incidentally is also the same as the 4th screen palette. Also, now what I thought was purple in the 4th palette is very much red now. Very confused :S
I have attached some pics to show what I am talking about.