I think I found a way to do it through models (rather than the API).
This code creates the product: http://pastebin.com/2L9snp4Z
The above code successfully generates a grouped product, assigns the sub-products under it.
However, when you go to view the product, it looks like this: http://i.imgur.com/2BVshN2.png
However, if I go to the magento backend, edit the product and save OR go into re-index all “Product Prices” - then the product looks normal (something that you can add to cart) as shown here -> http://i.imgur.com/cZCHAm1.png
Any idea why this is happening?
Have I missed a step in creating the grouped product manually via model?