In looking at the HKP paper linked to in the OP, the quoted uncertainty range is from H_o = 64 to 80. I didn't look at the paper in detail, so I'm wondering if that range is intended to be so-called "1 sigma" errors, or if they are "3 sigma". If the former, that allows H_o in the mid 80s without even contradicting the HKP. Also note that the error is almost entirely systematic, because their statistical errors would seem to average to a lower value, perhaps +/-3 or less, so the +/-8 they quote must be largely due to exactly the effects dgruss23 is talking about. As it is much easier to have a significant systematic error than a significant statistical error (statistics are much better understood than systematics-- the latter change with every major new discovery), it seems that H_o =80 is completely plausible, and even 85 would seem to be pretty hard to completely rule out. Even the HKP authors might well agree with that, I would expect.
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