Kyrgyz and Li Ling connection?

When the former Kyrgyz President (Akayev) was in power, he brought up a long known historical event in Chinese history.  During the Han Dynasty (over 2,000 years ago), a Chinese army under General Li Ling was appointed to march beyond Great Wall and subdue the Huns.  Having insufficient supplies and men, the General could not turn back or the Emperor will slaughter his army at the gates.  Instead, he accepted the Hun ruler (shan-yu, khan, etc.) offer of surrender and joined his nation.  The Huns sent Li Ling and his men to resettle somewhere in Altai mountains where ancestors of Kyrgyz lived. 800 years later when Kyrgyz stormed down from Altai to drive Uygurs away from Mongolian basin, the Kyrgyz arrived at Tang Emperor's court to remind them that they were partially descended from the earlier Han General Li Ling.  They say the Kyrgyz with black hair are from Li Ling Chinese while the red hair Kyrgyz are from the native Turkics.