Opening a Port

I have an application that is having troubles transmitting over the
internet and I suspect it's a firewall/ports issue. I had someone with
domain admin rights log in and test the same app and the had the same
problems. They tell me that with their credentials that they have
access to all ports and that something else other than a port problem
would be the problem. I thought that if a port is closed, it is closed
to everyone regardless of their credentials. Can someone confirm my
suspicion though that a port is closed regardless of your login
credentials?

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