Is Buddhism just Hinduism stripped for export? I was listening to a podcast featuring Alan Watts and he stated that Buddhism was Hinduism stripped for export. He also says it at more length in his book Buddhism the Religion of No Religion  ....


  Hinduism [..] is a religious culture. Being a Hindu really involves
  living in India [...]. You cannot be a Hindu in the full sense living
  in the United States or India.
  
  Buddhism is Hinduism stripped for export. The Buddha was a reformer in
  the highest sense: someone who wants to go to the original form or
  reform it.


There is a sense here of Hinduism being a culturally specific religion and Buddhism being it's universal equivalent. Is there any sense in which that is true or is 'Buddhism is just Hinduism stripped for export' just a pithy soundbite that actually doesn't mean very much?
While "Buddhism" is already quite a difficult terminus, since there is a host of sects, schools, vehicles and apart from that another host of indigenous practices that infiltrated Buddhism in places it went to, "Hinduism" is even more difficult.

Just an overview: 


The Vedas are the oldest scriptures of India, dating back to somewhen between 1800 BC and say 1000 or 800 BC. The Vedic Religion is a religion of sacrifice. These are important in so far as practically all Hindus consider the Vedas as holy scriptures and their religion based on it.
By the end of the Vedic Era, maybe 800 or 700 BC the first Upaniṣads began to appear and with them the ideas of an eternal individual soul (ātman) opposed to an all-encompassing world-soul (brahman), rebirth in an endless cycle (saṃsāra) determined by the deeds of an individual (karman).
From about 700 or 600 BC onwards there was a movement of people who tried on their own, to find a way out of the cycle of rebirth by meditative and ascetic practices, the so-called Śramaṇa-movement. Theoretically this movement was heavily indebted to to the Upaniṣads.


Buddhism ultimately developed out of this heterodox movement (the Śramaṇa-movement) and except for the person of the Buddha and the theory of no-soul/not-the-soul (anātman) shares almost all of the common features of this movement, namely denial of Vedic authority and rejection of the caste-system. The Samañña-phala-sutta gives a good idea of views held in this movement and the relation of Buddhism to these views.

Now, as it comes to Hinduism, "classical Hinduism", if such a thing exists, surely did not exist in that time. In Hinduism there are six orthodox systems of philosophy, the first of which, Sāṃkhya, developed alongside with Buddhism, maybe a little earlier, maybe a little later. All the other orthodox systems (Yoga, Nyāya, Vaiśeṣika, Mimāṃsā, Vedānta) developed later and under more or less heavy influence from Buddhism.

To give just on example: Nyāya is classically the school of logic in Hinduism. It was the theory of Pratītyasamutpāda, that generated a need for a deeper understanding of causation, conditionality and logic, which in turn gave rise to a development in logic in India and ultimately to Nyāya. Similar indebtedness has also been claimed for the Hindu philosopher Śaṃkara to maybe the Buddhist philosopher Nāgārjuna.

Now, Śaṃkara is also responsible for the Hindu renaissance in India and for the final i-dot on the Vedanta-system. What Hindus believe in today is in no mean way shaped by his thinking (although we should always keep in mind, that it is impossible to point to that which "Hindus believe in") and therefore ultimately by Buddhist ideas and developments in refutation of Buddhist arguments.

Getting back to the question. It is very true, that Hinduism cannot or can hardly be exported, it is bound to a priestly class which in turn is bound to India (Brahmins not being allowed to defile themselves by leaving India), it does not or does hardly convert (sects like Hare Krishna disregarded here), the gods reverred are rather local deities without universal appeal and so on. And on top of that: missionary zeal is rather foreign to it.

Buddhism on the other hand had this "missionary zeal", though not to be compared with the Abrahamic religions, right from the beginning, embodied in the Buddha's wish and urge to teach the truth he had found. So what is true in Watts is that Buddhism is much more universal(ly appealing) than Hinduism. But the quote of Watts somehow implies two more things, both of them being wrong:


That Buddhism is some sort of Hinduism. That this is wrong should have been shown by the above historical sketch.
That Buddhism was designed to be exported. This is wrong since Buddhism was not designed.


The equally polemic counter-attitude to Watts would be that Hinduism is just Buddhism flavoured with some archaic elements (reverence of the Vedas) and stripped of anything too hard to understand for common people (like anātman) and anything that might offend a priestly elite (like "equality of men"). Like Watts statement it is basically wrong with a pinch of truth in it.