Skimming per se is a substitute for ownership and control:
Prior to 1958, regulation of gambling in Nevada fell under the Tax Commission. Oversight was lax: Nevada politicians didn't care if gangsters were building casinos--they welcomed them because all they cared about was that the gangsters were bringing money and tax revenues into the state. Though their ownership and control of casinos was legal under Nevada regulation, most mobsters preferred to hide their ownership through front men (as in the GFII dialog you quoted) because they wanted to protect their assets from the Internal Revenue Service and the FBI.
After the televised Kefauver hearings (1950-51) and McClellan hearings (1957-58) exposed Mob ownership of casinos to a nationwide audience, the Nevada Legislature was forced to clean up gambling's image. In 1958, they took control out of the Tax Commission and put it into the new Gaming Commission. They gave the Gaming Commission two big teeth: the power to license "key employees" of hotels; and the "Black Book," a list of people who could be barred from even entering a casino, much less owning or operating one (that's the rule Nicky and Ace ran afoul of in the movie "Casino"). In effect, the "Black Book" drove Mob involvment underground. They were able to milk casinos through investments (like the loan from the Teamsters Central States Pension Fund that was detailed in "Casino") or threats, or violence. The end-product wasn't ownership or even control--it was access to the "skim." While the skim was profitable, it proved to be a poor substitute for actual ownership and control, which they had prior to '58.

Ironically, the "Black Book" worked in some ways like Prohibition did for booze--it helped create violence. Casino gaming in Nevada was relatively peaceful when the Mob operated more or less out in the open because they all knew what the others were doing, reducing jealousy and suspicion that are so often the causes of murder and mayhem. They had an incentive to keep things peaceful, the better not to scare away business. Driven to secrecy, mobsters fought each other far more frequently. Vegas declined.
That set the stage for Howard Hughes and his buying spree. His imprimateur, in turn, made gaming respectable for big corporations and hotel chains. Today's mob involvement in legalized gaming is a fraction of what it once was.