SQL Server : low disk space impacts CPU? Is there any relation between disk space and CPU utilization?

We experienced the issue with very high CPU utilization on SQL Server 2008. At the same time, we were in lack of free space on the server. Once we cleaned up some space - CPU utilization was back to norm.

Is this a coincidence or there is a documented explanation for this?
NTFS is susceptible to low disk space. When you fall below 10% file system drivers may start creating various bottlenecks (not only with CPU).