I still am not sure that "trivial" is the right level to rate the ability to bribe government officials is at. After all, each of those links points to a person charged or convicted of bribery, meaning that the people privy to the situation raised it with the authorities deliberately or through incompetence.
Thinking about what the collusion would look like here, I think faking the drawing (which is a well-publicized event) is more difficult than having a ticket printed after the numbers are drawn. In the latter case, who has to be "in on it" for it to succeed? It seems like an audit trail on each ticket would be sufficient, proving the time that it was purchased. It seems like this would require a lot of forged evidence in order to successfully pull off that scheme, and it doesn't require that the audit log be publicly disclosed.
Or at least, who is the winner of the lottery hidden from? Is it hidden from the IRS? Is it hidden from the disbursement department at the lottery? Is it hidden from the issuer of the original lottery ticket? These all represent groups of people who you would have to buy out in order to successfully collude.