Partly right. The information is not linked to your Bungie.net profile. It's linked to your gamertag. That said, if you're just going from 360 to One, as long as you are using the same gamertag you used on your 360 you shouldn't have any problems.
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Alright, I was hoping that was the case. If something goes awry I suppose I can just contact Bungie support, I took screens of my character on the mobile app as proof I was in the beta. Now I just have to figure out how to actually change my preorder.