Distance learning MBA is valid for Ph.D so need not to worry but beware. There are many private universities running degree scams.
Ph.D in India must be offered accordance to UGC regulation of 2010, yes you can pursue external Ph.D as well
I have written in detail about the whole process and list of the university please check following post
Human Resources, Business, Management and career questions blog.: How to identify fake, real, recognized and not recognized M.Phil and Ph.D degree in India
29th November 2013 From India, Mumbai