An Issue like that would be reported to Shopify VERY fast. You would see it on http://status.shopify.com/
The first thing to always do when a customer reports something like this as well, is to test it yourself. If a Customer has an issue with your website, but you, your friends, your family, and shopify don't..... Its more than likely the customers issue. Either an issue with their computer, or their internet, etc.