When a trained provider is required
Under 1926.50(c), when there's no infirmary, clinic, hospital, or physician reasonably accessible in terms of time and distance to the worksite, a person with a valid first-aid certificate — from the American Red Cross or equivalent training that can be verified — has to be available at the worksite.
In plain terms: if the hospital is more than a few minutes out, you need trained first-aid help on site. On most construction jobs that's the case, so there should always be at least one certified first-aid provider present, and enough of them to cover all shifts and work areas.