From what you are describing, I think that is the configuration that I have (more or less). I have 3 nics. One is connected to the modem, one is the private NAT'd network and one is connected to a physical switch which I use for strictly management.
I have attached a screenshot of my current setup.
vmnic0 is attached to the modem and is in vSwitch1
vmnic1 is attached to the internal private NAT'd network and vSwitch2
vmnic2 is attached to the management network and vSwitch0
If I understand you correctly, vSwitch1 only has a VM Port Group and no VMkernel Port, which means it shouldn't be requesting an IP address?
If that is the case then perhaps it isn't requesting for an IP address anymore and the address that they are showing is just residual.
EDIT: I should point out that ESXi shows that I have a name and a domain from my ISP which makes me think it is still requesting that information from the ISP.