What are the restrictions of using GPL linux as the base image for proprietary software?

I am going to build a docker image to deliver to customers. The image contains our proprietary software and, of course, some flavor of Linux which has a GPL license.
This now raises the question of distribution of GPL software, and whether or not this is OK from a legal point of view.
I read in some places that in this situation the image is considered an “aggregate” (such as a cd-rom) as opposed to a single product, and thus it is OK. Our software can remain proprietary as long as we acknowledge and refer to all GPL components - to their license and source code.
However, some people in the team still aren’t convinced so I wanted to ask here, if anyone has considered this issue before and what did you conclude?