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.
If the group is made up of UDT agents, then they clearly coordinate. If CDT agents are a small fraction of the group (assuming that transaction costs make perfect bargaining non-feasible for CDT agents, as usual), then UDT agents' (meta)-incentive to reject blackmail will be muted to some degree, depending on the fraction of CDT agents. The opposite consideration applies to the blackmailer's side: when faced with rejection, she has to expend resources on a costly punishment that will only affect the fraction of agents that's CDT. So her incentive to engage in blackmail in the first place rises as the fraction of UDT agents drops.
On a different note, assuming that the informational environment is favorable, the best response to "group blackmail" is probably not for each agent to reject blackmail individually, but for all agents to coordinate on incenting whomever can reject blackmail at lowest cost. Under this assumption, UDT agents will have an (meta-)incentive to incent rejection by any agents in their group, including CDT agents. But still, the main result is unchanged; as the fraction of UDT agents falls, the resources expended in providing such incentives will drop proportionally.