I'm not sure about specific US legislation but "made in the USA" and "product of the USA" would imply to me as a consumer that the item had, as a minimum been produced in the USA but I would also feel misled if a significant proportion of the ingredients were imported. In the UK it is illegal to mislead a consumer with labelling and the legislation is written in these vague terms. I suspect that some manufacturers would use the term "product of the UK" if not using any UK ingredients but I wouldn't like to defend it in court in the UK, the US may be very different. I suspect that if you're using a large proportion of US ingredients and only minor ingredients are imported (only due to the fact they don't grow in the US for example) then it's probably easier to defend but I'm definitely not an expert on US law.
As for how to establish it? Ask your suppliers to give you a supply chain map of where they have sourced their ingredients and get them to agree not to change this without prior approval. It's not always easy to get the information from your supply chain but you need to demonstrate to the auditor that you've tried. A supply chain map can be as simple as:
Grown in A country by B farmer
Processed by C manufacturer in D country
Exported by E exporter to the US
Sold to our company by F agent or broker