Are you arguing lottery fraud is rare? Seems pretty common to me and not just in the US.
But in the US, where even the elections are computerized, anything is possible.
https://en.m.wikipedia.org/wiki/1980_Pennsylvania_Lottery_sc...
What is more common is to pay a winner more money for the ticket than the prize, to claim the prize for oneself, as a money laundering scheme. But this is not solved by removing anonymity, as it's hard to prove the scheme without the other person saying anything.
An probable example of this (in Spanish): http://www.levante-emv.com/comunitat-valenciana/2012/02/19/c...