That has the same effect on other sort of games as well. Let's say that instead of investigation, the player was looking for potions and said, "I've heard rumors of these Moon cultists - it's said they brew powerful potions on the night of the new moon, to sell to those who are in need." The player is still creating the solution to his need, even if that need isn't information.
But is that allowed? It might be in SOME games, but there are many possibilities:
In 4e it isn't specifically allowed, and depending on how you approach the rules, may be completely disallowed. If you play 4e ala [MENTION=42582]pemerton[/MENTION] then a player could make something, a Religion check maybe, or undertake an SC, to find out if the Moon Cultists make potions as stated or not. Failure will have consequences, success will probably establish this as lore.
In HoML you MIGHT be able to use Inspiration to create a plot element like "A Moon Cultist approaches me with a potion of Shadow Walking to sell" BUT the character would have to have some attribute which could be leveraged to explain narratively WHY this came to pass (and the player would still have to come up with that explanation). The player could also undertake an SC to try to find such a potion, but its not established that they will dictate the narrative terms, or that Moon Cultists will result.
In Dungeon World you could utilize the move Spout Lore. You would have to use it in a very specific way however to significantly constrain the GM into producing Moon Cultist lore. Other moves might be required in order to actually achieve said potion. 'Complications' and 'Costs' are likely to be involved, which are going to lead to the GM making some (probably soft) moves. These might include some unsavory features of said Moon Cultists, lead to finding the ENEMIES of the Moon Cultists, etc.
I'm not sure how this might play out in games [MENTION=42582]pemerton[/MENTION] is more familiar with, I'm sure he could explain how BW and Cortex+ would likely handle it. I'd think in both games that potions of whatever sort are wanted would need to be plausibly tied to at least one PC's beliefs or milestones.
Now, in PACE, you could pretty much do it, but again it would probably hinge on a success of some sort. Like you'd have to figure out where to go, which might involve overcoming some sort of obstacle. Assuming a PC has a relevant attribute rated they can probably do so at some cost.