On a trumpet? A clarinet? No, the motions don't simultaneously overlap. The fingering mechanics are slightly different at speed, but you would still start slow while using the higher speed mechanics and tonguing technique, not jump into high speed practice first.
No one is saying not to practice slow first. This advice is specifically for intermediate or advanced students who are putting a focus on developing speed specifically. Practice slow first, increase tempo slowly next, but when you hit a plateau, you need to add some repetitions that are well outside your comfort zone. You need to feel what it feels like to play fast, then clean it up.
It seems like this is a far more time efficient methodology to build speed on guitar, I do not know why it wouldn’t apply to other instruments like trumpet.
