If you buy back existing shares of stock, you increase the value of each share of stock by improving the earnings and free cash flow per share. (Think of it as paying down long term debt.)
Stockpiling the money--especially that much money--doesn't generate much return for shareholders. Sure, it earns a little bit of interest, but Buffett's reasoning is probably that there are better places for that money. Use it to make the company worth more.
If you own say 1% of a company and the company buys back 50% of its stock, then you will end up owning 2% of the company with the same shares.
Currently for each apple share you get ownership of a part of apple's business and a part of apple's huge stockpile of money. The business would hopefully grow and create profit for a long time to come (at least you believe that if you own the shares), but the cash would sit around and do nothing. If you think that the business is undervalued, than it is very much in your benefit for apple to swap your share of the cash for an additional share of the business.
Instead purchasing shares has other benefits, such as certain tax concessions (e.g. franking). To increases in the capital value of the shares purchased which can then be sold for a net profit. Additionally holding shares (especially large numbers) gives you certain voting rights to how a company is run. This is why certain wealthy individuals are known to purchase stock in public media companies. (There are examples were some media influencing has taken place.) You can also lease your shares/work with short sellers for gains. (which is trying to earn money via speculating the movement of the share price.)
A bit more on short selling: (this is grossly simplified)
Short selling is the idea of selling shares that have not been purchased beforehand. Let's say Person A sells person B 50 shares at $1 each, however after the deal is made the share price drops to 50c each. Person A is able to scoop up the 50 shares for half the price, even though person B is contracted to buy them for $1. In effect a decrease in the share price has given Person A a profit. My example sounds a bit fraudulent (selling something that you don't actually have.) In the real world it involves leasing shares and the idea that shares will be available to buy at a later date. Porsche famously bankrupted many short sellers /speculators by quitely buying up all the spare VW shares. (Something they deny publicly.)
This chart is "industry life cycle" so let me apply it to smart phones.
There are 4 distinct phases:
1) Pioneering Phase: Back in 2004sh, a number of companies were making barely usable smart phones: (Pocket PC, Palm Treo, Black Berry)
2) Growth Phase: This is where we are now, Apple, Google, Etc. are all building products targeting this market and it is growing like crazy.
3) Mature Growth: This will happen in the next 10 years, (my guess is in the next 5), as the world population who can afford phones is limited and there will be so much product with limited new customers. Companies will still innovate, and sell product, but the growth rate will slow.
4) Stabilization and Deceleration: This will probably happen after people in impoverished nations get cell phones and all Smart phones are driven down in price. (Think current PC market) and who knows what will cause the deceleration? I don't.
--Here are the theoretical flows of capital for each phase--
1) Pioneering = VC, Private Equity money flowing in to businesses
2) Growth Phase = IPO, and Private Equity money flowing in to businesses
3) Mature Growth Phase = Companies start buying back shares, and paying dividends.
4) Stabilization Deceleration Phase = Bankruptcy, Buyouts, continue paying flat dividends etc.
What you will notice is that between 2 & 3 share holder money starts getting returned. Growth companies are priced "high relative to current earnings" but "low relative to distant future earnings".
Investing in the growth phase is done so that the stock will appreciate as certainty over product success becomes apparent. Once that happens, the stock price will be much higher as the market expects dividends.
Apple is a great example of this process.
I'm not ignoring the effect; I'm just not viewing it in vacuum.