Yes, that's a reasonable summary. I think there were good reasons for that (excellent reasons for not looking at transmission, for example: how could they?), and by getting results against minor illness they had good reason to think that would extend to protection against hospitalisation and death. The trials could have had hospitalisation and/or death as endpoints but of course they'd have then needed to be longer, delaying use of the vaccines.
And the absolute risk reduction is surely not what anyone should care about. The risk for individuals varied wildly with age (and other factors), so absolute risk reductions would have very limited value. I can imagine they could also have publicised age stratified risks of hospitalisation and deaths (which did happen to some extent). I'm also not sure how people in general feel about a 1% chance of dying; personally I'm rather keen to look at a vaccine that will significantly reduce a risk of such a cause of death. Vaccination also seems to reduce the risks of long term sequelae (presumably by reducing the chance of infection and the severity of infection); hospitalisations and deaths are far from the only risks of infection.