How likely is it for something that says 'perishable. keep refrigirated.' to make someone sick if they eat or drink it after it sits out for over 12 hours?

Consider the example of a quart of milk. If it is at the end of its sell-by date, or has been previously opened/contaminated, more likely to cause a problem if left on the counter after breakfast.

In that scenario you could get ill from eating perishable food that's left out in room temperature as bacteria start to multiply quickly in such a setting.