@R.E., why would it be different than buying something that needs B.Y.?
BTW, here is a different scenario.
Here is an excerpt by Reb Moishe Heinemann:
Can bishul Yisroel be achieved by setting a timer that will ignite the oven at set intervals?
No. Since the Yehudi does not perform direct lighting of the oven it would not qualify for bishul Yisroel. In commercial settings (e.g. hotels, hospitals or factories) where large boilers provide the steam for the cooking equipment, bishul Yisroel requirements would be fulfilled if the Yehudi flips a switch or presses a button that directly ignites a boiler.
If the action that is done by the Yehudi causes an indirect lighting of the oven, that action would not qualify for bishul Yisroel. Hence, dialing a number that in turn trips a switch that in turn lights an oven would be considered a “grama”, an indirect action that would not qualify for bishul Yisroel.