With these sort of mechanisms, what we "think" or "believe" or "feel" is of no relevance, we need to focus on the evidence and symptoms, do some diagnosis and testing and then confect a solution.
It sounds to me like Devlo are guessing a bit and it's a guess some of us here might have made on the prima facia evidence. Multiple DHCP Servers on a SOHO network is a "bad thing" and certainly something to check out. You should only have one DHCP Server and unless you really want to get into the weeds with DHCP and IP addressing, it's best if it's the DHCP Server in the router that terminates your ISP link.
Technically, a DHCP Server could be anywhere (and you can have more than one of them,) but the DHCP Servers in SOHO kit often lack the granularity of control required to deploy one elsewhere, so unless you really want to get your IT nerd on, it's simplest to use the ISP router's DHCP Server and accept the default values it will offer and make sure any others are turned off.
To know for sure what your Sky box does, you'd need to check it's spec. An IT nerd, such as I, could use a packet sniffing tool (like WireShark) to check out the actual network traffic, but that's a pretty sophisticated tool that's not for feint hearted!
Multiple DHCP Servers of itself isn't a "problem" for someone that knows what they are doing - the issue is that in SOHO kit, the IP leases those DHCP Servers hand out almost always designate themselves as the "default gateway" (ie the device that connects to the Internet) and thusly you could have hosts with different and competing default gateways (some of which may not even reach the Internet) - which would be bad.
In IP networking, every host on the network is taught a "default gateway" IP address. Either by manually assigning one or automatically as part of the DHCP Lease. The "default gateway" IP address is where any host sends traffic it does not know what else to do with (ie it cannot figure out how to deliver it locally.) In small SOHO network the default gateway is almost always your ISP router (that's what routers do - forward or "route" IP traffic towards it's destination,) and thusly the DHCP Server loaded into most SOHO routers are shipped configured so that they always designate themselves are the default gateway in the DHCP Leases they serve out. And in SOHO kit, we usually cannot change this. (In "big boy" DHCP Servers managed by IT pros. we can dick around with this sort of thing.)
If you look on a Windows machine, for example, open up a CMD prompt and run an IPCONFIG /ALL and find your active NIC, amongst the IP addressing information you should find it's own IP address, the subnet mask and the default gateway (amongst other stuff.)
If you have multiple DHCP Servers, then they could be serving out leases that conflict with each other and this sort of thing would change, seemingly randomly, and stuff would start dropping off the Internet.
EDIT - Whilst musing over this, the thought occurred that it might be an interesting experiment to give your plugs static IP addresses (ie manually assigned,) if they allow it, rather than letting them get their IP using DHCP (if that is what the are using now) and see if that makes any difference. We can probably walk you through the process.