I can't even begin to count the times people have done this to me. I tend to be one of the slower emergency drivers on my department, mostly because I spend a lot of time watching for people to do exactly this. Some days I'd swear someone turned the truck invisible. You would think a 50 foot long, 60,000 pound ladder truck, painted bright red, covered with strobe lights and reflective striping, with two air horns, two electronic sirens, and a mechanical Federal "Q" siren wouldn't be too hard to notice.
As much as we carp about the apparently deaf little old ladies, all kinds of drivers cause us problems. We have the guy on the cell phone, busy mom trying to corral screaming kids, people who have their music so loud they can't hear us, and on and on. My personal "favorite" is the driver who, oblivious to us behind them, can't figure out why all the cars ahead of him are slowing down and pulling over. Look, everyone's pulling over for me! Of course he then pulls to the left to clear them and directly into my path.
Of course, some just can't bear the inconvenience of missing the stoplight, so they squeeze through the intersection just ahead of us. Might have had to wait an extra minute at the light otherwise, and we just can't have that. One incident that really sticks in my mind (I wasn't driving for this one) was when, while running lights and sirens, we swung wide into the left lane to gain clearance for a tight right turn. As we started to swing right, the driver and I simultaneously saw two cars of teenagers passing us on the right. One of our best drivers was at the wheel that day, and only his quick reaction kept us from wrecking two civilian cars and a $700,000 ladder truck, likely with severe injuries or loss of life.
Same rules apply on the road as in tractoring: take your time, don't get in a hurry, and pay attention to what is happening around you.