Am I being paranoid?

I am really surprised you didn't cause a fuss about some odd person coming into your room at 2 in the morning.  I would have been on a witch hunt if it were me. 

When I had Libby my husband talked me in to leaving her in the nursery during the night so we could sleep.  I was extremely lucky in the sense that Libby took a bottle and nipple with no problems, so they would feed her formula during the night so I could sleep.  I never had any sorts of problems breastfeeding, which was nice.  When I went to the nursery to pick her up I had to show my wristband and it had to match Libby's, otherwise I couldn't have her.  There were always more than one nurse in the nursery at a given time, there got to be quite a few babies in there even though we were in a very small hospital.    I would leave the baby in the nursery so you can actually get some sleep instead of being worried about who is coming in your room.  Just make sure your hospital has some sort of precaution on who can take the baby from the nursery.

I think I would have caused a fuss if I would have been in my full complete state of mind. I'm glad I was with it enough to know to say NO though. The weird thing too was that people were in and out of the room all night long, it sucked but didn't seem odd since the nurses were in and out all the time anyway. I had complications with my C section last time so I think I was more out of it and then also more staff was in and out of my room too.

I know they put matching bands on me, my husband, and the baby. I remember them saying to make sure to keep the baby in the basinette when leaving the room otherwise they get suspicous.

I totally forgot about that.  We were not allowd to be walking to halls with the baby in hand.  We had to have the baby in the basinette any time we were out of our room.  I walked quite a bit because I was told I would heal faster from my c-section.  So, I had Libby at 11:20pm and was up walking at 5:30 or 5:45 am LOL  The nurse thought I was confused and still drugged because I got up so early and I left my room on my own.  I just couldn't wait any longer to see my precious baby.