Hi,
At least in my system, a ProDesk Hewlett-Packard 600 with a i5-4570, hyperthreading support is reported by speccy as "Supported, Disabled". This is wrong because i5-4570 doesn't support hyperthreading. Just check this link:
http://ark.intel.com/es-es/search?q=i5-4570
It seems that in i5-4570 processors only is supported hyperthreading in i5-4570T and i5-4570TE, while the others (i5-4570,i5-4570R and i5-4570S) can't support it.
Regards.