Correct. In theory it doesn't make much of a difference (ie, 20 nickels vs 4 quarters). Investors generally perceive it to be management having a bullish outlook on stock price. And there is a small liquidity benefit (although AAPL already pretty liquid).
Options markets are where this has the most impact. In order to sell a covered call, I need to own at least 100 shares of a stock. A stock priced at $500 or higher (in the case of GOOG) makes it harder for a smaller investor to participate in the options market. Splitting the stock price makes it possible for a little guy to purchase options based on their stock holdings.
Have you traded the minis? I just looked after reading MichaelApproved's comment and the quotes I saw for the minis were way outside the standard contracts.
Well they're not usually "way outside" but yes, they are usually more expensive. Also, most brokers add a per-contract fee so that also adds to your cost basis.
If you're looking right now, it's possibly because AH trading is much more volatile.