I have spoken to many people about this over the years. The factory techs that seem to have more than your average clue have told me that the Honda stuff is formulated specifically to be low-moisture absorption ... so it won't degrade like "lesser" DOT3 or DOT4 fluids. I think some of the DOT4 fluids out there give up some of this protection in favor of higher initial boiling points.
Why? I think Honda's afraid some folks don't maintain their cars well enough and are concerned about degradations in basic braking performance caused by very old, very degraded fluid ... a very real concern, IMHO.
I've used both Valvoline Synpower and Castrol LMA (both DOT4) in my Hondas and Sentra SpecV with terrific results. No leaks, loss in braking performance, corrosion issues ... no problems at all. As '03 EB Corvette Z06
states above, OEM branded stuff is overpriced and I am not into lining Honda's pockets when I can simply buy quality aftermarket parts and fluids elsewhere.
So, buy good
aftermarket stuff and change it regularly (every year or two) and skip out on the OEM brands whenever possible.