Why doesn't PostGhost just record tweets using the browser? I'm sure it can be done without much problem. This is blatant abuse by Twitter. Public tweets are public, and the readers should be able to record/screenshot/save them, without Twitter having a say in the matter.
If they don't allow using the API for that, use the browser directly.
Using a 'browser' from their base-of-operations in an automated manner would fit the definition of scraping, which is not allowed by Twitter's TOS.
I wonder where that line is drawn. A person using their browser, clicking a link to load a web page initiates a hundred different automated routines[1]. Is that not automation? Is it then automation to have a click initiate another click or two more clicks? Where do you draw the line?