Good posts, DanielLion and Bankei.
In about 2,600 years into this dispensation it is unrealistic to assume that somewhere along the line there was never
some break in the lineage for bhikkhus either. At some time along the line there certainly must have been some preceptor with a parajika offense or some other thing making him ineligible, but that does not change the conviction in the heart of the person receiving the ordination and the subsequent men or women who followed and their conviction and practice with the Dhamma.
By focusing too much on the letter and the rules the only outcome is less worthy people ordaining or perhaps no one being allowed to ordain and the sooner the end of the Dhamma / this dispensation.