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.
It's quite common for elderly patients' relatives to threaten me with all kinds of time consuming or reputation hurting bullshit like complaints involving a lot of paperwork or bad press in the local newspaper unless I wedge their relatively healthy granpa straight from the hospital past the line to a nursing home as fast as possible, instead of sending them back home where they'd do just fine. I haven't caved in and so far nothing bad has happened except some relatively harmless badmouthing. It's common for doctors to be blackmailed to do all kinds of stuff like unnecessary investigations or treatments.
You could say that in the US there have been enough trials and press gone badly for doctors that blackmailing often works. I'm glad that this isn't the case in Finland and we're still practicing cost effective medicine instead of covering our asses from all angles out of fear. The flip side of this is that incompetent doctors roam a bit too freely.
In a couple of cases I've made decisions that I've been blackmailed to make, not because of the blackmailing but because the blackmailer's interests happened to coincide with my medical reasoning. I find this problematic for signalling reasons.