I don't believe that is necessarily so at all. Just because the Louisiana lottery was corrupt doesn't mean it would be easy to fix a modern lottery. I also challenge the notion that "state" employees are inherently more virtuous or altruistic than private sector people.

Selling the franchise to operate the Lottery does not mean that the private operator would follow any less stringent security procedures than today's lottery employees do - and I would imagine that the state AG or some other regultory body could (and should) take responsibility for ensuring they do so.

Your example makes my point. A private operator would have just as much incentive to protect the security as the state does - and maybe more since the private-sector people involved can be sued/fired if they don't perform. God knows a lot of lottery staffers aren't/can't be fired if they don't. Everyone knows if they screw up and a concern arises over security, people will stop playing and there goes the chance to earn any return on your fat, up-front investment. 

Your point would be well taken IF lotteries had mechanical ball drawings that were televised and there are multiple potential witnesses. Since many lotteries are computer drawn and there is no way of knowing how the drawings really work it would be very easy to rig.

Remember a lottery doesn't just have to be rigged so someone wins it can also be rigged so more people loose. The latter may be far more profitable for a private company and hard to detect with computer drawings.

this would be a very bad idea......