Yes, doctors "in training" do assist and do parts of surgeries. That is how we create our future cardiovascular surgeons. However, an actual surgeon is always in the room or around the area of that OR for emergencies. They must master the entire part of the procedure, so there will be some surgeries where they do most but not all, depending on their level of expertise. They often let them assist much more on people who have not had past heart surgery. They do that because people who have had heart surgery may have more complicated issues with opening up and closing, as well as identifying what is what when they open. It's not this open, obvious space with people who have already had cardiac surgery. They must identify what is what (due to masses of scar tissue) and that requires the expertise of a certified cardiovascular surgeon. Don't worry though, no student doctor that doesn't have many, many years of experience is allowed to touch your heart. They must earn the right to be a part of someone's delicate organ such as the heart through learning. Training programs are also heavily regulated by certain organizations, which includes on-site review.
debster913- you are right, they do often have fellows start the femoral artery catheter access point. The femoral artery is not very big and the catheters inserted are much bigger than the artery itself, but since arteries have elastic properties, they can use big catheters. It is a risk of any cardiac catheterization that the artery becomes damaged, which can lead to peripheral vascular disease. If you are having symptoms of numbness, tingling, weakness, burning or aching in your right leg- consider contacting a vascular surgeon. They can evaluate any damage to your femoral artery and recommend the best treatment option. PVD increases your risk of heart-related issues such as heart attack, so it may be worth your while. They don't always do surgery for femoral artery claudication/occlusion, they can now do stents that open up that artery. However, bypass of the artery is also an option. I've had that myself 2 times, going on 3 next Friday. Yes, it was do to catheterization damage.
Best of luck!