That seems untrue. On the Cloud side every .Net shop I know from startups to government/enterprise are now deploying to Linux or Linux containers.
On the developer side 75% of .Net devs are on Visual Studio on Windows but a big and fast growing segment are using JetBrains Rider on Mac/Ubuntu.
Not everyone who uses Azure is a "Microsoft shop", in terms of programming tech stack. Plenty of people use Azure as a cross-cloud redundancy play, or because they do business with Amazon competitors that refuse to have their data on AWS.
It's the reverse in AWS, they have a bit more Windows market share than Linux. And he also backed up your statement.
His take (which was just his speculation) was that the virtualization stacks ran those OS's more efficiently. HyperV with Linux VM's and KVM with Windows VM's. I have no idea if that's true or not.
If you plan on shipping server software, I expect it to run on Linux, particularly in a container.
.NET definitely has first-class support on both Linux and Windows.