Yet that was enough hint to help Claude solve the puzzle. The great thing about this hint... is that you can always give it to yourself."

Not credibly and not with the actual information content that the brother's utterance provides. That leaves the question of whether and in what circumstances it is instrumentally rational to self deceive in the direction of optimism bias (or optimism regarding the relative merit of rechecking the low branches for more fruit instead of climbing higher). Some considerations:

• Humans have all sorts of biases against doing the kind of tasks that a beginning graduate student has to do. Because evolutionary speaking (and possibly colloquially speaking too, for that matter) it's probably a crazy thing to be doing. Assuming the academic qualification has been adopted as a goal, however, overriding the long term focus problem with mental hacks is nearly a necessity.
• It is more beneficial for others in my society to systematically take risks (in this case of time and potential) than for me to take risks. This would lead me to expect advice of this form to become common wisdom even were it slightly bad for the recipient.
• The hint given is sufficiently ambiguous as to be a nudge in the direction of various discrete strategies. This includes "think from the perspective of your model of various other suitable people" which is popular advice itself (with some credible studies backing it).
• Mild social competition can be a useful focus for some people's problem solving skills. Conceivably the imaginary social competition could help too.