I'm not an expert, but index funds still purchase the stocks, so when the active investor bought a stock at an increased price, it would increase the market cap and so the index fund would buy some more of it from them.

Nah, because the value of the stock that the index fund already owned would also increase in the same proportion.

Fair enough, for stocks the index already owned, but what about for the others? If the investor took a stock that wasn't in the top 500 and inflated its value above the 500th stock, wouldn't an S&P 500 index fund then buy it?

It's a thought experiment.