I think you're talking about "scare quotes". Per Wikipedia: Scare quotes is a general term for quotation marks used for purposes other than to identify a direct quotation.
Generally, if quotes are used within quotes, then the single quote would be used. Sometimes the single quotes are used even if they are not within double quotes. Depends upon the style. (I tend to use single quotes quite often, to sorta indicate that the words are not actually "quoted".)
You can look up the LameStreamMedia style books, if you want to find their take on it, but they certainly aren't the definitive word on punctuation, grammar or anything else in the English language, since they bend anything any way they feel they want to. Remember Mark Twain's comments:
...That awful power, the public opinion of a nation, is created in America by a horde of ignorant, self-complacent simpletons who failed at ditchdigging and shoemaking and fetched up in journalism on their way to the poorhouse."
--Mark Twain, License of the Press, A Talk Before the Monday Evening Club, Hartford, 1873.
although I feel he went too lightly and was much too politically correct in that thought on them. Then again, he did say:
"If you don't read the newspaper, you are uninformed; if you do read the newspaper, you are misinformed."
--Mark Twain (1835-1910)
Even during the civil war, the military weren't particularly enamored of them either:
"I hate newspapermen. They come into camp and pick up their camp rumors and print them as facts. I regard them as spies, which, in truth, they are. If I killed them all there would be news from Hell before breakfast."
--Civil War General William Tecumseh Sherman
Of course, ol' Thomas didn't think highly of them in his time, either:
"Advertisements contain the only truths to be relied on in a newspaper."
--Thomas Jefferson to Nathaniel Macon, 1819
Then there's a somewhat more contemporary view:
"The essence of American journalism is vulgarity divested of truth."
--Winston Churchill
Thank you.