I noticed that runners playing on the Gameboy Player don't get the "Health & Safery Warning" screen when they reset the game mid-run. Is this a natural property of the Gameboy Player, or is that due to the GBI mod?

There are two types of reset, one is to press the reset button on the game console, and the other is to input a specific command (soft reset) You can soft reset with A + B + START + SELECT buttons

Thank you!!!