When dealerships use those checklists, a lot of mechanics check the items as "good" before they even bring your car into the shop. That saves time and it reduces handling the paperwork with dirty hands. The thinking is it is not very likely such a new vehicle is going to have a problem with those things. Once the car is on the hoist and they see something that is not okay, they have to change where they checked the item.

In this case they may have been working in the area of that boot and could have accidentally damaged it. You might consider getting a second opinion from a tire and alignment shop. They regularly replace boots and half shafts, and we can often tell what caused the damaged. If it's a hard rubber or plastic boot, they often split at the seams or sharp points. Those splits will follow those grooves and will be straight. If the hole looks like the rubber was smashed and mangled, that comes from crushing it with a tool or metal part. Simply bumping it or prying against it won't do it. That kind of damage is done too on some poorly-designed cars by struggling to remove a power steering pump or generator when access is limited, or some similar service. To intentionally or accidentally damage a boot that way takes quite a bit of effort.

Some boots normally seep a little grease and an experienced mechanic would ignore that. The work you had done can be done by any new mechanic who might believe that seepage is not okay. To know for sure, get a second opinion.