Was the influence of Taoism on Buddhism responsible for the development of Mahayana? In this Partially Examined Life podcast the presenters stated that when Buddhism moved into Chinese it naturally was influenced by the pre-existing Taoist philosophy which is uncontroversial. However they then when on to make this stronger claim that 


  it was the influence of Taoism that was responsible for the
  development of Mahayana.


That is quite a claim and obviously the real position is more complex. However is there any truth in that statement? Was Taoism instrumental in the development of Mahayana Buddhism?
It is hard to assess half a sentence without a wider context, but I would interpret this as "it was the influence of Taoism that was responsible for the development [but not creation] of [some branches of] Mahayana[, more specifically, some of the Chinese ones]". And in this form the statement is true.

You seem to interpret it as "it was the influence of Taoism that was responsible for the development of Mahayana [in India, even before it reached the Chinese soil]". Which is a false statement.