'The president pro tem of the National Assembly hammered his gavel, trying to restore order."
I'm a bit rusty at this, but I'm pretty sure this comma is not being used solely to indicate a breath, although a breath is called for here.
In very rough terms:
President (noun) hammered (verb) gavel (direct object) -- main clause
trying to restore order -- is a phrase (which is why you can't just separate the two bits with a period; a phrase lacks the grammatical requirements to be its own sentence). I'm not sure what it is exactly because it's been a while since high school grammar, but I'd guess it's some kind of adjective phrase since it's describing the president's motivations.
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The grammar rule that I expect you are thinking of is the one being broken in this sentence:
He opened the door, firing the gun.
Which you would rightly call incorrect because the comma indicates that the two actions are occuring simultaneously -- when in fact they are happening serially. This sentence should be revised to:
He opened the door, and fired the gun.
Where you could probably cut the comma, but that's an artistic thing.
However, in a situation where the second part of the sentence is an adverbial or adjective phrase (as the one you provided above), or where the two parts really are occuring simultaneously:
She turned to run away, yelling as loudly as she could.
then the comma is appropriate.
People sometimes rant against putting "-ing" verbs after commas, because they get sick of seeing the incorrect construction that implies simultaneity when the events are in fact serial. However, when they do it without giving context for the rant, they end up confusing people.
This is the same thing that happens when people rant about passive constructions such as "The ball was thrown by the boy" and you end up with students of writing damning all forms of "to be" as being in passive voice.
As to whether big name authors get away with bad grammar -- well, I don't think it's actually an issue. There are lots of region variations. Regional variations and typos would account for maybe 90% of these things. The rest have usually, in my experience, reflected someone's misunderstanding of a grammatical rule. As a culture, we in the US are pretty fuzzy on grammar.