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Velorien comments on Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102 - Less Wrong
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This depends very much on how people conceptualise the philosopher's stone. If they go "by following these instructions, I will create a stone that produces the elixir of life and is also capable of permanently transmuting base metal into gold", and the philosopher's stone does not in fact do these things, then yes, they will fail.
On the other hand, if the wizard in question is aware that they have no idea how such an artefact is supposed to produce the elixir of life (or indeed what the elixir of life is beyond its expected function), or how it's supposed to transmute things, then their thought will surely be more like "by following these instructions, I will create an artefact that will deliver great benefits unto me, its possessor". Which ought to be sufficient to succeed if "for enemies" is.
If so, surely at least one of the many wizards to attempt the philosopher's stone ritual(?) must have been contemplating a sufficiently broad possibility space to succeed. And yet this does not appear to have been the case.
For further evidence, consider how frequently people learn and cast the Patronus Charm despite the fact that they are completely ignorant of how it really works.
Although people are ignorant of why it works, people casting the patronus charm know exactly what it does. It makes a silver colored animal that makes fear go away and can chase dementors.
As to conceptualization, you may well be right that it could be done without understanding the mechanism but with correct conceptualization. But, I bet most wizards don't have the right conceptualization. And worse, I bet most wizards investigating the philosophers stone have a Theory. And their theory is probably directly wrong which blocks them from being able to do it.
This does sound very likely. Although it's worth noting that there are at least a few powerful wizards who are, if not rational, at least capable of processing evidence without leaping to conclusions - we hear them described at the conclusion of Hermione's trial.