No flips for you!
Sure. I see a strong version of the player's action where he just asserts these stones are like the ones back home and that he's activating them according to the rituals he's observed. While this still runs into the player introduced fiction problem (and 5e's lack of tools to really address it*), it's a much more clearly defined action that can have more obvious downsides (the stones aren't like back home and you've done something bad, you've messed up the ritual and something bad happens, you've started the ritual but something's off and you better figure it out right now or something bad happens, etc.).Agreed. I like that the player has offered up some interesting backstory that may be useful later, but I just can't see the reason for an ability check here. I'll just provide more information.
I kinda feel like this play looks more like other games that encourage player-side fiction propositions that the mechanics then test to see if they're true or not.
*I say this because 5e really focuses on altering odds through bonuses and have mechanics like seeking advantage that can really sway the likelihood of success. Also, the DM's tool of DC adjudication is a bit off for setting a DC on if something is true or not, so the tools on the DM side are weak as well. Most games that favor player-side fiction introduction use a mechanical system that has relatively fixed success/fail odds for everything and strong player-side tools to mitigate failures. This lets the DM really push hard on failures and introduce more tension into play by thwarting player propositions to the fiction and introducing negative aspects because the players can mitigate them. In D&D, the closest similar tool is really the hitpoint.