I honestly think the best take away from that story (outside of her clearly unethical response) is that she's an absolutely trash leader who can't even properly raise a dog - a state or the country are far beyond her skillset.
I think you broke the code yes. I think it's moderately likely that "get your hands dirty" will become a phrase we hear again in the somewhat-near future as shit gets more and more real leading up to the election.
I'm not saying that at all as a good thing, just where the GOP seems to want things to be heading.
"Having the strength to do the dirty work" has been a euphemism for committing selfish, barbaric atrocities for...forever, basically. A lot of the people prosecuted for Abu Ghraib used similar justification, for example.