Militia and Combined Arms Attacks

I'm 90% sure we played this correctly, but I wanted to post it as a question to make sure I didn't miss something.

If an Artillery and Militia Infantry unit engage in a combined arms attack, then all Saber dice results are treated as misses, correct? That would seem logical, since all MI melee results ignore Sabers.

The same would then hold true for combined arms attacks using Austrian Grenzers, British Rifles, or Russian Cossacks.... No Saber Hits.

This rule is clear in the rulebook

In a Combined Arms Combat, even though the artillery unit
may not be in melee, each saber symbol rolled will score a hit.
However, when an artillery unit engages in combined arms with
a unit that does not hit on sabers in melee, the artillery dice added
to the melee will also not hit on sabers.

And if you want to know where exact, search it, because this helps always to become safer about the rules

Hoo boy. I looked everyplace but the rule book. I'll start there first, next time.