Can you help?

Not really, you can ask me anything here - chances are if you need to know others will benefit as well.

You've pretty much worked it out. The data nodes you sell are not the node access products, but some other nodes that you've used a nodeaccess module (such as this http://drupal.org/project/nodeaccess) to disable the default access to. Obviously the people need to be able to access the products in order to pay for them. Don't use the permissions page as that is outside the realm of node access, and this module will not be able to override that - you have to use a node access module.

When I created the product I only pointed it to one story, but completing the purchase opens up all of the stories on the front page.

We need to look into this more, either that is a bug or a bad configuration somewhere. Have you done that whole node access rebuild thing?

Mate I've never used skype, nor do I like to make phone calls, even to my mother. I will unable to help you that way.

Here's a weird detail: each product is displayed once to the admin account but twice to the fake test user's account.

Displayed how/where ?

Can you tell me exactly how you have configured the product?

What did you use to disable access for the users that haven't purchased the items?

Could caching be interfering?

the generic permissions to block access

That doesn't sound right! Permissions and node access are two different things. If they don't have the permissions they will never get the access.

nodeaccess module to give individual grants to nodes

So all the purchasable nodes have individual grants to someone? When a user has not purchased -they don't see it?

The fact that it's the products themselves appearing twice, not the data nodes people are buying suggests you may have confused the two at some point during configuration.

There is also the possibility that the menu does not correctly reflect node access due to caching. Perhaps just make yourself a list of links to the nodes and try to click them and see what happens. Ultimately a reliable way to 'list products' is using the Views module - it tends to respect node access when pulling up listings.

Well that depends on your purposes, as long as it is a module that works on nodeaccess it should be fine. The thing about nodeaccess is you don't block access with it, you grant access with it. You have to grant somebody the access (author/admin) and it will automatically deny access to others.

this one is good for restricting access for all nodes in a content type to a certain user role: http://drupal.org/project/nodeaccess
this one is good for restricting by taxonomy instead of content type: http://drupal.org/project/tac_lite

I've also made one based on the cck user reference field in a particular node, one where you have access to nodes if you type in a secret password into your user account, and one that gives you access to a node if that node references a node you have access to. Those are probably way too specific to be useful for you though.