So if you are having problems accessing data with a parametric data request here are a few solutions and the reason you are having problems:
The reason: Excel Services requires read AND write privileges to the excel file you are trying to access with a parametric data access request, like the example below:
1. Creating a domain account to be used in the IIS SharePoint application as the anonymous account with anonymous access to your public site
As the title suggests create a new domain account that you are going to use instead of the out of the box anonymous account assigned to your public site. Then you will grant to the needed file read/write access from you SharePoint user interface. The other reason why you need a domain account is that excel services requires claims tokens to authenticate and authorize a user to access information. This procedure is not going to suit your needs IF you do not want to allow write access to your excel data or other security related issues that prohibit you from using this method.
Your steps: Go to your IIS 7 => Navigate to your web application => Go into the IIS area in your application and open the Authentication option:
Next Select “anonymous”(this should be enabled if you have a public SharePoint site), select edit from the left options panel and change the user to your newly created domain user.
2. Option two is to go around the problem programmatically. Here is one example from the following link that might do the trick: