Does a banana really taste different if you eat it with the peeling on or off?

I opened a banana today for Saige, but apparently it was the wrong way. So she threw herself on the floor and exclaimed she was NOT eating that banana. She insisted that I open another one, which, to my demise I did. After taking the peeling off this time, she again threw herself on the floor and in tears exclaimed, "that is not how you eat a banana." I now had two full bananas on my counter and wasn't about to open a thrid. Does it really matter, I asked her. You don't even eat the peel- only the banana. We went through many different scenarios of how you could possibly eat a banana all the while she was crying and yelling. After about ten minutes of this I came to the conclusion that her banana had to be completely peeled, but not broken. Then placed back in the peel so she could hold the peel while she ate the banana. I ask again- Does a banana taste different eating it with the peeling on or off?