I remember my Anesthesiology rotation a 4th year. With the past as a tech, attendings were impressed I was able to run a diagnostic/leak check on a machine without help. I was double checked, of course, but still, not a skill you normally have.
As for the practical of providing anesthesia during that time: I did a spinal case with just the attending watching about a week into the rotation. He only gave advice and talked through as I placed the spinal, gave a light sedation, and monitored the patient. Taught all the way about balancing sedation and extra pain meds as the patient needed it, and physiology behind it. Stayed with me until we got the patient to PACU. Patient was aware, was more than accepting of the situation, and was quite pleasant throughout the entire procedure (and yes, I was introduced as a student.)
Ballsy? You bet.
Was it nerve-rattling for me? Absolutely.
Ego boost that an attending would let me do that? F**K YEAH!
Would I do it without an attending behind me even if I make it into CA-1 slot? Oh, HELL no!
The idea is to see if you are confident, not cocky. Confident is to realize you have the skills and understanding to do the job. Cocky is when you think you skills are perfect and nothing will go wrong. "No Fear" in this profession kills quickly.
Yes, the attending was minimal in hands-on, and I got to show him I could do the work. Although more than a few times, I must have looked at him like a deer in headlights when he said, "Go ahead." But he was always there, making sure I wasn't boxing the patient, and pimping me on the whys and the physiology.
I agree with periop: If the attending trusts you with a task, trust your attending will stop you before something bad will happen. And don't forget to ask questions if you are unsure of how to proceed. Enjoy.