Thanks for providing this additional note.
The URL rewriting happens prior to Sitefinity's execution. By using it, you're essentially overriding Sitefinity's native handling of URLs. This is perfectly fine and very powerful, but once it's done, there isn't really anything the Sitefinity can do to override your rules.
Here are a couple of random thoughts:
1. Remove the URL rewriting pattern and begin managing all the ~/product/ pages in Sitefinity. You could create external page links and point each external page link to whatever URL you wanted.
Example: ~/product/1234.aspx redirects to ~/Results.aspx?ProdId=1234
This is a very easy solution, but it might be cumbersome to maintain if you have TONS of links.
2. Make your URL matching pattern less greedy so it doesn't get applied to ~/product/ pages you're attempting to create in Sitefinity.
Now the URL rewriting pattern only gets engaged if the product page is proceeded by an underscore. Example:
If the page doesn't have a leading underscore, then the pattern won't be engaged.