The Bontrager H5 tire is a pretty thick hybrid tire with a puncture protection layer under the tread. This puncture protection layer is either very thick, very inexpensive, or possibly both, because it's not very pliable. I have a set of 35mm H5 tires on one bike, and have ridden them in 26x2 size, and they're the opposite of "supple". I can see how someone would describe them as "rock hard" if pressing straight down on the tread -- there's very little give, even when the tire isn't even mounted to a rim!
I'd probably ride these just like the OP is -- in the 35-45 psi range.