Thank you for you comment, red clay. Your comments are valid. So let me try to answer them:
Once cooking technology with hot stones was invented it can be adopted, changed. I also believe that people new how to cook in water before they invented baskets and pottery. Have a look at
Once you develop the knowledge about how something works you can change it. Use pots instead of lined holes....Also technology is transferable. Once someone invents a technology for grinding acorns it can be used for grinding anything...The grinding stones can be brought from forest areas to grasslands and swamps and can be used for grinding what ever food needs to be ground there. When grains became dominant starch foods the same grinding stones were used to grind them. Acorns and nuts were collected and used together in all the early cultures together with roots and other starch carrying plant parts. But acorns were so dominant as a food source that this is why I believe that they probably played the dominant role in the invention of all the mentioned technologies. Not the sole role...
I hope this makes it a bit clearer.