I always try to read and assess the Partition as a total
mess up (rather than good/bad thing) which is root cause for the current volatile political situation of the subcontinent from two angles.
1)Concept of partition
2)process of partition
I think Congress is responsible for first one and both All India Muslim League, British were responsible for the second.
Reasons for mess up (Concept of partition) : Not giving proper representation to Muslim Community.
The Congress Never made serious efforts to enlist the Muslim community in its struggle for Indian independence, which made part of the Indian muslim Community apprehensive; which led to the concept of partition to be born.
Reasons for mess up (Process of Partition) : Process of Partition was too quick for the then apprehensive people of the country.
Muslim league:
Leaders were not firm (confused ?) in their demands; whether to for Independent Country or For greater Autonomy for Muslim majorty Provinces in a united India (Even though Idea of seperate state for Muslims in India was hatched in 1930, picture was only clear to the people of the country only in Lahore Resolution during 1940 from where active campiagn for Pakistan was started. Still untill 1944 there were attempts by Jinnah and Gandhi to reach a single-state solution. !!).
(Hindus and the Muslims belong to two different religions, philosophies, social customs and literature.... To yoke together two such nations under a single state, one as a numerical minority and the other as a majority, must lead to growing discontent and final destruction of any fabric that may be so built up for the government of such a state....Jinnah At a League conference in Lahore in 1940). If this was his argument then why did he try for a separate country from the beginning itself ? why he still tried to negotiate for a greater autonomy in united India till 1944 ?
British:
The british after world war 2 were totally exhausted and wanted to get rid of the mess in subcontinent; by washing their hands as quickly as possible (As shown in documentory by OP). They failed to ensure smooth partition to take place by providing adequate time frame for migrants from both sides to cross the border under proper Law and order condition. After all it was their duty as they have ruled subcontinent and robbed wealth through excessive taxes and other means.
However if you analyse the results of partition today, I personally think concept of Partition itself was good for both India and Pakistan. It filtered out the people who thought that hindus and muslims cant live together, from Republic of India for good, and fulfilled the aspirations of Pakistanis who got seperate country according to their wish. But the scars made by partition process still haunts.
However time is the best healer for wounds created, and its better to forget the past and look forward for future.