At a GrandAm race at Barber years ago, there was a tire carcass on the track after turn 5, just a few yards in front of my station. We'd just had a yellow and the field had only been running a couple of laps, so race control basically said, "You will have 40 seconds to go get that and throw it over the barrier and get over yourself, is that enough time?" I told them it would be, so I was on a live track, with race control monitoring the leaders, and we cleared it without having to go yellow again so soon after we'd been yellow. I grabbed not only the tire carcass, but a couple of rather significant pieces of metal.
My point is, it was all planned and communicated. Had I taken too much time, they would have thrown a yellow before the cars got to me, but it wasn't needed. The marshal running across the track may have well been sent by race control, and not going on his own resolve.