I agree with @pichlo that the given scenario is the one most widely used by any appliances that are "internet enabled"; however from my point-of-view it is just as badly flawed as could be!

Even if there was no sinister ulterior motivations from the manufacturer who so wants to become more of a service operator then just purveyor of HW I'd feel extermely uncomfortable to allow it.
It's an intrusion to my home if external parties can access the information provided by appliances and potentially control them and/or upload firmware or configuration to the devices.

What I'd do is to try to figure out the protocol that the device wants to communicate with homebase and write my own counterpart for it, running it locally and diverting the traffic from the device to it.