Your situation involves personal contact with an object in air (lancet, maybe fluid, maybe blood etc. ). You will be happy to learn that you had no risk, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal with a penis, neither of which you did and you didn't share hollow needles to inject with which is the only other way to acquire hiv - there are only 3 ways to get hiv. Analysis of large numbers of infected people over the 40 years of hiv history has proven that people don't get hiv in the way you are worried is a risk.
HIV is a fragile virus in air or saliva and is effectively instantly dead in either air or saliva so the WORST that could happen is dead virus rubbed you, and obviously anything which is dead cannot live again so you are good. Blood and cuts would not be relevant in your situation since the hiv has become effectively dead, so you don't have to worry about them to be sure that you are safe.
There is no reason for a person to test when they are safe. The advice took into consideration that the other person might be positive, so move on and enjoy life instead of thinking about this non-event. hiv prevention is straightforward since there are only 3 ways you can become infected, so next time you wonder if you had a risk, ask yourself this QUESTION. "Did I do any of the 3?" Then after you say "No, I didn't" you will know that it's time to move on back to your happy life.
No one got hiv from what you did during 40 years of hiv history and no one will get it in the next 40 years of your life either. You can do what you did any time and be safe from hiv.
The other person's status is irrelevant when you have no exposure.
I highly doubt your doctor would spread disease through bad practices anyway so you probably are mistaken, but in any event it isn't an hiv risk per the above.