Always follow manufacturers recommendations, specially when it comes to primer specs or brand. They know their equipment's limitations.
I've had a primer blow on me back in 1989, and I cannot remember if it was on the Pro1000, Dillon 550B or Hornady Pro-jector. Fortunately it did not start a chain reaction.
My opinion is if the primer seating operation is away from the primer feed or primer magazine, then it is safe to use any primer brand. An example is the Lee Turret T-bar system as mentioned above. With the Safety Prime attachment, the primer magazine is at least 4 inches away from the seating operation, safe enough IMO.
For example, on a Dillon 550B, the primer tube is a few inches away from the primer seating station, so I consider that a safe set-up or design. As an extra safety precaution, the Dillon's Primer tube is shielded by a thick steel tube that should direct any primer chain explosion upward away from the operator.
However, the primer feed/magazine and seating set-up in a Lee Loadmaster are just a fraction of an inch apart. This design can cause a chain explosion should the primer in the seating station go off. This is the reason I believe Lee is warning against using Federal Primers.