(In all the following, I'm assuming there isn't a vast difference in casing flexibility between the two tyres. But there's rarely enough difference anyway between two models to over-ride the huge volume factor of 28mm versus 23mm).
"Proper inflation" can be whatever you want*, but if you want the same effect in your wide tyre as you get in your narrow tyre, then your wide tyre has to be inflated to a lower number of PSI than what you have in your narrow tyre.
It's not just about rolling resistance. Higher casing tension means the tyre flexes less, which makes it less comfortable. A 28mm tyre at 100 psi is much harder than a 23mm tyre at 100 psi - as you can feel simply by squeezing the sidewalls with your thumbs. It doesn't make sense to use the same pressure for both these very different sizes, unless you want very different effects from each of them.
ALL of the effects of an inflated tyre depend on the ratio between volume and pressure, not pressure alone.
* Though I suggest the ideal is a good compromise between rolling resistance, grip, durability and comfort.