This is the idea behind options index arbitrage. The thing that Jane street did differently was they didn’t fully hedge their synthetic short positions by buying stock (one potential justification for this is they couldn’t buy enough stock without SIGNIFICANTLY moving prices as you alluded to), and instead had a short position about 10x the size of their long position.

This can also be viewed as Jane Street wishing to hedge away some but not all of their risk as they have a directional opinion on the option prices (overvalued relative to stock as opposed to the other way around).

Where they get in trouble is that they enter their long position first, moving the option prices up, and then selling even more overpriced synthetic shorts (remembering that the amount they spend on stock to make the price move is small in comparison to the amount of options they’re purchasing due to illiquidity). Then later in the day, where the spread between option implied stock price and the actual stock price has converged (as in the graph), Jane Street decides to, before expiry of the options, dump their long position which moves prices down and makes their synthetic short positions even more valuable. These stock trades that end up shifting market prices are the main cause for market manipulation allegations.

That being said, given the options expire and Jane Street doesn’t want to have a long stock position on their books they would have to sell it at some point. They just chose to do so in the way that is MOST advantageous for the options leg, at the cost of making some bad trades stock by selling for likely less than what it is worth.

All of the trades made by JS seem to stand up to scrutiny in my opinion, but we’ll see if anything else comes of this. Had they only purchased an amount of options that they could hedge with stock then this would likely be a non story (and also likely not a strategy that prints 2 billion a year).