The strength training fatigues the neural muscular componet to the point where your system does not fire with the same strength, the same cooridnation, etc. Which creates ground contact issues, muscles doing work they are not supposed to do, and all of that creates opprotunity for injury. Strength training on the other hand does not suffer the same issue when running in front of the lifting because you can work around the parts not worked while training.
"Nature hides her secret because of her essential loftiness, but not by means of ruse." -Albert Einstein