Aumann's agreement theorem -- I don't claim to know all its generalizations -- assumes that the two parties have the same priors, and that each knows the other's "information partition" (i.e., what states of the world the other can distinguish). It also assumes that their knowledge of one another's posteriors is "common knowledge" in a technical sense. It also assumes that both parties are perfect Bayesians and that this too is "common knowledge". I see no reason to assume that any of these is true, given MBlume's description of the situation. (In particular, the assumption regarding what each knows about the other seems to me, from Aumann's description, to imply more detailed knowledge of one another's cognitive faculties than any human has of any other's.)

Clearly someone is failing (very broadly understood) at something, since at least one of the two doctors assigns 99% probability to something untrue. But, e.g., the following is perfectly consistent with the scenario as described (although unlikely):

Both doctors are superlatively intelligent, skillful and well informed (about medicine). Both have done the same, entirely sensible, tests; one has been the victim of extreme bad luck and got evidence at the 99.5% level for a wrong diagnosis. Both have also been victims of further mischance, and each has (unknown to the other) got evidence at the 99.5% level that the other is horrendously incompetent even though that is not actually true. (We can agree, I hope, that all this is possible, albeit very unlikely?)

Now each considers the evidence. A, before learning B's verdict:
P(malaria & B incompetent) = 0.995^2 ~= 0.99
P(malaria & B competent) = 0.995 . 0.005 ~= 0.005
P(bird flu & B incompetent) = 0.995 . 0.005 ~= 0.005
P(bird flu & B competent) = 0.005 . 0.005 = 0.000025

Now for a Bayesian update based on B's opinion. Some kinda-plausible figures:
P(B gets given result | malaria & B incompetent) = 0.1
P(B gets given result | malaria & B competent) = 0.001
P(B gets given result | bird flu & B incompetent) = 0.1
P(B gets given result | bird flu & B competent) = 0.99

So the new odds are roughly 0.099 : 0.000005 : 0.0005 : 0.000025, giving a probability of about 99.5% for the "malaria & B incompetent" option.

B goes through an exactly parallel calculation, favouring "bird flu & A incompetent".

Both doctors have been unlucky, but neither has been irrational. Those who think Aumann's theorem requires one of them to have been irrational given the data: please explain what's impossible in the above scenario.

To be fair, I did neglect to state specifically that we have common knowledge of our probability estimates

"Well, it need hardly be said that someone here is failing at rationality."

Right, using the agreement theorem, someone is failing at rationality. Either it is him or it is me. I must conclude that it is him. (If you would like an argument for this, I can provide it, but will skip for now as I suspect it is uncontroversial.)

Given that I have already concluded that my colleague is irrational, I cannot trust him to make a rational decision regarding the choice of drugs. Thus I just need to make the choice that will save at least 5,000 lives. (Note: I cannot predict which decision he will make, since irrational reasoning can lead to either choice. But if he chooses the malaria drugs, then all for the better.)

After we both choose the 5000 of each drug,

I don't think you can claim to have acted rationally.

What is the "you" here? If the "you" is plural and refers to both me and my colleague, it is expected that we did not act rationally since we already knew we weren't both rational.

However, I acted rationally, given the information that my colleague would not.

By the way, what is the interpretation "around these parts" of Aumann's disagreement theorem taken together with the fact that apparently rational people have different solutions to these kinds of dilemma's? Is the idea that eventually, we'll reach a consensus?

I generally assume that the people who read my comments are capable of detecting obvious errors.

Look at the requirements for those theorems to apply, and then look at the conditions MBlume set out.