I agree with Son of Horus about this:
It says that "...some units can move and fire heavy weapons. Such units can charge after firing." To me, it sounds like if you can fire a heavy weapon on the move, you'd be able to fire a rapid-fire weapon on the move as well. It says "such units..." so it seems to me like they just have to meet either requirement.
It does not say "...charge
after firing heavy weapons" so, if you adhere to purely what is written they can fire then charge any weapon; whether or not that was intended to be the case, adding a condition that is not written is not strictly RAW.
However, I disagree with him about this:
The only people who are rules nazis are people who can't paint and are insecure about not only losing, but losing to someone who actually is good at the hobby.
That's my experience, at any rate.
Some people are stricter or laxer on rules purely depending on whether they feel animus toward their opponent: if they face a fluffy army they are tolerant of everything including rewinding time to do something you forgot; if they face an optimised fluff-ignoring list then they will challenge every possible advantage.
Also. one man's overly strict rule challenge is another man's defence against cheating.
Ultimately, real legal systems with proper consequences have no solved the problem of ambiguity, so I have no expectation that GW will resolve it; it would be pleasant if they published general definitions and proper rules of interpretation for terms in the next editions though so that, amongst others, wording in one book really was a guide to meaning of rules in others.