Yes, babies a few hours old can actually feed on colostrum. They won't get huge quantities - probably around 5ml, but that's all they need at this stage. Lots of babies do nod off after a few sucks in the first day or so, but ideally you want them to be actively feeding at the breast for at least 10 minutes. Some babies hardly stop even in the first day!
Having said that, I don't know how they would know whether this particular baby had fed or not - it's very difficult to tell unless you have somebody who knows what they're doing actually observing a feed and/or you're checking blood sugars.