The beauty of buying back shares is that you don't need to "keep it up" as much, because you're not beholden to shareholders as much...
Apple buying shares doesn't make the rest of the shareholders have 100% of the company. It makes having 100% - what_apple_bought%. They would still own 100% of the outstanding stocks, but those stocks don't represent 100% of the company's equity/ownership anymore.
The fact that the shares are destroyed (as shares) shouldn't matter, if it increases the part of ownership Apple has on itself.
The purpose of a stock buyback is to reward shareholders by increasing stock price. The increase is caused because of the reduction in float. Each share represents more of the company after the buyback than before. [1] If that wasn't true, then the share price wouldn't increase, and there would be no reason to do a buyback.
The bought back shares could be kept by the company as treasury stock, but the company can't vote treasure stock or pay dividends. [2] The outstanding shares represent 100% ownership of the company.
So to say that stock buybacks make companies less "beholden to shareholders" compared to dividends is just wrong. Dividends and stock buybacks are exactly equivalent except for tax treatment (and possibly market pressure).
[1] https://en.wikipedia.org/wiki/Share_repurchase [2] https://en.wikipedia.org/wiki/Treasury_stock
If that shell company would be owned by Apple, it implies the outstanding shareholders would own that company, including all the shares it holds in Apple, too.