If I remember correctly, the locomotives also have a speed control mechanism where brakes are applied automatically if the engineer overspeeds over a certain threshold.
There is a system on the locos like that, however it only applies to the maximum authorized speed for the trains entire run. For example, the top speed for the Empire Builder is 79 MPH, so the computer is set to hit the brakes if the engineer exceeds 83 MPH or goes over 79 MPH for an extended period of time. But if that train just happens to be traveling in a 59 MPH zone, the computer is unaware of that so an engineer could technically go 65 and the computer wouldn't care.
Positive Train Control (PTC) fixes that issue and allows the engine's computer to know what that the maximum authorized speed has changed.
On the Southwest Chief, there are a few places where the train can go 90 MPH. So again, the computer is set for that limit. So when the train is running in a 79 MPH zone, or a 59 MPH zone, or anything less, the computer won't stop the engineer from speeding.
However, as you mentioned, there are logs on the engines that would still catch it. Additionally, it is not uncommon for the host RR to put someone alongside the tracks with a speed gun to try and catch speeding engineers. And unlike a driver in their car, the penalty isn't a ticket. It's suspension and quite possibly a career ending banishment from ever operating an engine again on that host RR's tracks.
So most engineers take great care not to exceed the track speed.