From what I know, Vista kernels (6.0) OS were delivered with IE7, and Se7en kernels (6.1) OS even with IE8. That means, as your Server 2008 R2 has 6.1 kernel, there NEVER ever could be IE6 on that machine!
IE detection relies on some registry entries, I guess. If they are filled with wrong information or even are missing, that could lead to such situations.
Some questions:
1. Is that server maybe a Server Core edition?
2. Could it be that IE is disabled in Optional Components selection? In 6.1 OS, IE is truly removed (executable and regkeys deleted) except the Trident engine required for other functionality. Detection would then fail (detect 0.0.0.0 or wrong version).
2003 server work because IE does not get updated.
2002 and 2003 kernels (5.1 and 5.2) cannot get IE9 at all.