Microsoft's relationship with linux is actually a bit more complicated. It was a top 5 [1] contributor to the linux kernel in 2011 and a top 20 [2] contributor in 2012. The reason here is because linux virtualization is a big deal for Microsoft Azure.
Although the rational here is fairly clear: having good linux support for Azure helps Microsoft sell its cloud service. Having good linux support for Microsoft filesystems helps people move away.
I'm aware of Microsoft's Linux kernel contributions; I've also been around long enough to remember the woes of NTFS compatibility, CIFS compatibility, the Halloween documents, the "virus" accusations, the SCO debacle, and not least of all relevant to this current conversation, the fact that exFAT is basically banned from an FLOSS implementation due to onerous licensing and software patents.