The heuristic that one should always resist blackmail seems a good one (no matter how tricky blackmail is to define). And one should be public about this, too; then, one is very unlikely to be blackmailed. Even if one speaks like an emperor.
But there's a subtlety: what if the blackmail is being used against a whole group, not just against one person? The US justice system is often seen to function like this: prosecutors pile on ridiculous numbers charges, threatening uncounted millennia in jail, in order to get the accused to settle for a lesser charge and avoid the expenses of a trial.
But for this to work, they need to occasionally find someone who rejects the offer, put them on trial, and slap them with a ridiculous sentence. Therefore by standing up to them (or proclaiming in advance that you will reject such offers), you are not actually making yourself immune to their threats. Your setting yourself up to be the sacrificial one made an example of.
Of course, if everyone were a UDT agent, the correct decision would be for everyone to reject the threat. That would ensure that the threats are never made in the first place. But - and apologies if this shocks you - not everyone in the world is a perfect UDT agent. So the threats will get made, and those resisting them will get slammed to the maximum.
Of course, if everyone could read everyone's mind and was perfectly rational, then they would realise that making examples of UDT agents wouldn't affect the behaviour of non-UDT agents. In that case, UDT agents should resist the threats, and the perfectly rational prosecutor wouldn't bother threatening UDT agents. However - and sorry to shock your views of reality three times in one post - not everyone is perfectly rational. And not everyone can read everyone's minds.
So even a perfect UDT agent must, it seems, sometimes succumb to blackmail.
Courts are generally heavily booked, trials take forever, it's a perennial news issue that courts are underfunded (this seems to be a major factor behind the incredibly nasty and abusive rise in 'offender-funded' court systems & treating traffic violations & civil asset seizures as normal funding sources to be maximized) and I've seen estimates that as much as 90%+ of all cases resolve as plea bargains. There's no way the court system could handle a sudden 10-20x increase in workload, which is what would happen if prosecutors stopped settling for somewhat reasonable plea bargains and tried to throw the book at suspects who would then have little choice but to take it to trial.
(I recall reading about an attempt to organize defendants in one US court district to agree to not plea bargain, overloading the system so badly that most of the cases would have to be dropped; but I don't recall what happened and can't seem to refind it. I'm guessing it didn't work out, given that this is almost literally the prisoner's dilemma.)
Oh, sorry, I think I was unclear or probably even confusing. I didn't mean prosecutors actually just ship off all suspects to the courts with a long list of charges. I meant that they threaten everyone.
Obviously, a plea bargain makes things much easier for prosecutors so their usual goal is to obtain one. However if the accused is sufficiently stubborn, their choice is (a) to assemble a case and prosecute for a few charges; or (b) to assemble a case and prosecute for many charges. I don't think there is a major cost-to-prosecutors difference between (a) and (b) so they go for (b).