What actually happened was
1999-February and early march
Gen.Pervez Musharraf held a series of secret meetings with the senior commanders of the PA at his farmhouse outside Rawalpindi, here they pulled out a plan that had originally been devised in 1975 to strike at Kargil, the plan was to sever Kashmir in half by holding the Kargil heights using PA commandos in disguise and then sending in Mujahid to capture Ladakh.Over a series of meetings where all the important (read loyal to mushy) corps commanders in the PA are briefed on the draft plan and asked for suggestions to improve on the same.Musharraf wanted to avenge 1971 nothing more nothing less.
1999-early April
Pervez Musharraf briefs Nawaz Sharif on the plan to take over the Kargil heights, nawaz is in a disadvantageous position with most of the army loyal to Musharraf he fears a backlash if he disapproves of Kargil and hence gives the go ahead.Also briefed is Gen Khwaja Ziauddin longtime family friend of Nawaz Sharif who was made ISI chief due to his political connections.
1999-early may
PA regulars and jihadist volunteers infiltrate into and take control of Kargil heights.
1999-June end
The CIA picks up intelligence that the PA has started to prepare nuclear missiles for launch against India without overt political approval, this information is passed onto Sharif.
1999-4th July
A scared and overwhelmed Nawaz Sharif flys into Washington bringing his family along as if he were flying into exile.here at a closed door meeting at Blair house on Pennsylvania avenue President Clinton Berates Nawaz Sharif in the strongest terms and literally orders him to pull back forces from the line of control or else....!Nawaz Complys and orders a withdrawal from Kargil ,he feels that by doing so he shall make Gen. Musharraf look like a loser in front of the PA's elite and hence smoothen Gen. Ziauddins rise to COAS instead the brass rallies around Musharraf.
I would take whatever Gen Ziauddin has said with a grain of salt, Gen Ziauddin was an engineer in the Pakistan army not a position from where you can become Dig ISI or COAS.However he was married to the daughter of a wealthy , politically well connected family in Lahore and his Father in Law just happened to be buddies with Buddies with Nawaz Sharif's father. It was the senior Mr Sharif that tapped Zia as a favorite brigadier and asked his son to promote the young man to army headquarters where Gen Zia got a chance to work with Pakistan's nuclear weapons program. when sharif made him Dig of ISIin the fall of 1998 he was widely regarded by the PA brass as an emissary of the Prime minister!