Well truth is, Wiring for these cars are complex and at times confusing.
Funny thing is there is a Ground says for headlights that is at Splice 150 and goes to Ground 101 that is under the hood. Your saying they were talking about inside ground. Only ground there is main ground for both highs and lows. It goes through the Headlight Relay to the Multi Switch and out to the Headlights. So my guess this is what they were talking about. About being some cluster connection for this I am not sure where or what part they would be talking about. There are 2 Dist off this on the path to/around the Headlight Relay. Main Ground here is G201 goes to Splice 236, This splice has 2 areas plus the one for the Relay that are Distro areas.
However one thing is if there was a bad ground both High and Low wouldn't work. DRL would because the DRL works from a different ground First one stated in this post here. G101 via Splice 150.
About the VIPER Alarm. I have installed many Alarms and many Aftermarket systems in cars over the past 30 years. VERY RARE that one is going to have a draw on a system. Most issues with Alarms is if they were installed wrong, or someone lives on a street where there is loud pipes going by always setting off the thing. Even then it could be setup in a way that isn't a problem. About connection to the BCM and the Viper making that fail. There is something other then the Alarm messing with your BCM. Unless again it was installed wrong and they cut wires when they were trying to splice into the wires.
Glad your Lights are working now. Hope you get everything else sorted soon.