MacBook Air mid 2011 Geekbench results too low
I went to the Apple Service, where the guy has booted from an external hard drive and run the Repair Disk Permissions task from Disk Utility. That solved the issue!

Note: I did run Repair Disk Permissions before while trying to solve this problem, but it apparently couldn't fix some of the files due to that the disk was mounted. So, booting from an external disk is crucial here.