Yes, it can scratch. Even stone tile can scratch.
It is not, scratch proof.
The only way you would know if they really did put 3 coats, is if you supervised them each step of the way.
No, it will not necessarily be shiny as an ocean's surface nor like a mirror.
And over time, the polyurethane will need to be redone. It wears away over time.
And, if you wear shoes in the home, everyday, tiny minute dust or dirt is in the house on the floor, and this itself, can scratch a floor's surface.
When we have contractors or workmen working on our home, and we had flooring installed recently... I ALWAYS supervise them, ask them questions, and see what step they are on or doing along the way. I have.... a construction background. I know, what it entails. And I see/watch what is going on in my home.
After the polyurethane was applied and it was completely completed, it also has to cure... and completely harden. This does not happen in 2 hours. And until then, even after 24 hours, you need to tread lightly.