I've been thinking about this topic for a while, and got into it in detail on Jonah Keri's podcast last week. In short, most leagues require outright collusion, i.e., one team purposely making a bad trade with another for some outside consideration, in order to veto a trade. In practice, that standard is almost never met - few people in friendly leagues are corrupt enough, for example, to agree to split the winnings at the end of the year in exchange for an advantageous deal. Instead, most bad trades that distort league outcomes are of the negligent variety.
For example, one owner is in 10th place and has virtually no chance of winning. He hasn't made roster moves every week, and he's even left healthy players on his bench and injured ones in his lineup for a week or two last month before remembering to swap them out. The other owner is in second place, in a dogfight for saves and deals the 45th-best outfielder to him for an elite closer. While the 10th place owner could conceivably make up more ground in hitting stats than he'll lose in saves, he didn't even run the numbers to find out. He mostly agreed to the deal because the owner asked, and it was no real skin off his back to say yes. When pressed on why he made the deal, the 10th place owner vaguely says something about liking the outfielder before the season and thinking he has upside. But he admits he's not that engaged in the league and hasn't done the math to see which player would leave him better off. He also admits not shopping the elite closer around to other teams who are in contention and battling for every save.
Plainly there's no collusion here - the 10th place owner isn't getting a cut of the winnings. But this trade should absolutely be vetoed, barring a convincing explanation showing the 10th-place owner did his due diligence and honestly believed this trade was likely to benefit his team.
The analogy I like to draw is to a trustee managing a beneficiary's money. Under the law, a trustee has two duties: loyalty and care. The duty of loyalty is breached if the trustee embezzles funds from the trust or "borrows" them to pay for his personal expenses and pays them back later. The trustee is financially and criminally liable for stealing from or improperly co-mingling funds that ultimately are for the beneficiary. This is akin to outright collusion. It's purposely subverting the purpose of the trustee-beneficiary relationship, just as paying the 10th place owner under the table to trade you his best player purposely subverts the relationship among competing owners in the league.
But the duty of care is breached if the trustee, for example, invests the money recklessly in penny stocks and complex derivatives in which he has no expertise rather than safe vehicles like index funds and highly-rated bonds. Just as the beneficiary could sue the trustee for embezzlement, he could also sue him for losing all the money with reckless day trading. Put plainly, the trustee did not exercise the requisite care and diligence in managing the beneficiary's money. This is akin to the example above where one owner disproportionately improved a contending team without seriously attempting to extract adequate value for his own. Just because the 10th place owner didn't purposely subvert the implicit agreement between league owners doesn't make it any less damaging to the league.
In sum, if we want to have trading leagues the outcomes of which are not unfairly distorted, commissioners should be able to veto deals for breaches of loyalty (collusion) and breaches of care (failure to make adequate efforts to extract even subjectively reasonable value.) To pass muster, a trade need not necessarily be one with which people agree, but both owners should be able to give convincing accounts of why they believed it was in their interest and show they made reasonable efforts to extract what they deemed to be fair value at the time.
For a separate primer on trade etiquette, click here.