No, it's not an irrational stretch. The example you cited is a case where your job and employer are directly relevant to establishing your credibility on that issue. A better example would be if you send a letter to the letter, giving your position and place of work as an engineer, on an issue like the Federal tax code that has no relationship to your job, your employer or your expertise. In this case, listing your job title and your employer serves no purpose other than to drag your employer into a matter that they may have no interest in getting involved with.
Tat is all still a personal inference.