I don’t think that “agenda” is a concrete enough concept to reason about. I think it would be better to ask something like:
If someone has a strong motivation to believe a particular proposition, is that proposition more likely to be wrong?
The answer there is trivially no. Obviously the correctness of the proposition is irrelevant to whether or not we are motivated to find it. For example, “smoking doesn’t cause cancer” is wrong independently of what financial motivations tobacco companies might have.
Put another way, the probability of a proposition being correct is not affected by random people’s interests. The probability of the correctness of “smoking doesn’t cause cancer” is the same no matter what tobacco companies would prefer.
However, there is another angle, which is to ask:
If someone has a strong interest in believing a particular proposition, are they more likely to believe that proposition independently of its correctness?
The answer here is almost certainly “yes.” Tobacco companies are certainly more likely to believe that “smoking doesn’t cause cancer” because of their strong financial motivations for reaching that conclusion. Or in other words, the more motivated to believe a particular proposition someone is, the less surprised we should be when they end up believing it.
But doesn’t that mean that the tobacco company’s interests make their conclusion more likely to be wrong?
No What it means is
That a motivated party believes the proposition is not evidence for the correctness of the proposition
Or in other words, the more motivated to reach a particular conclusion someone is, the less we should take their evidence into account when considering the proposition for ourselves.
Edit: providing an example
Imagine I were considering the proposition “smoking doesn’t cause cancer” and thought the chances of it being correct were about 50/50.
You might tell me “the tobacco companies believe smoking doesn’t cause cancer, but have huge financial interests in that conclusion.”
I would not say “Well lets ignore their interests! since they believe it, I’m inclined to agree and say that it is most likely that smoking does not cause cancer.”
I would also not say “Well, because they are so strongly interested, they are probably wrong, so I think smoking probably does cause cancer.”
What I would say is: “Well, it’s no surprise that they believe what they are motivated to believe, so it doesn’t tell me anything. My probability is stuck at 50/50.”