Is it true that even a well trained Doberman can not help running after someone or something when it runs?

No, a well trained Doberman, if commanded to do so, will sit on a freeway until it gets hit by a car. Around 1900, a cross was recorded in the Doberman ancestry with a black greyhound. The greyhound is a sight hound, bred to hunt small animals by running them down. There is also significant Manchester Terrier in the Doberman’s blood. These dogs were often used to catch rats.

This composition leaves the Doberman with a high propensity to chase and catch things. However, the Doberman’s primary breeding is for an obedient temperament. If your Doberman gives chase inappropriately, that is what the ‘No’ or ‘Leave It’ command is for.