This vulnerability is considered "low" and has a CVSS score of 5.0. The pen test takes an existing page and simply changes the verb in the submit, passing the form payload in the query string. If the web site raises an error, or displays a page that is different from normal, it is a PASS. If the web site returns a page that is substantively similar to the normal page, it is a FAIL.
Handlers for POST requests often have different mitigations; for example, CSRF is often implemented for POST and not for GET. By changing the verb, an attacker could potentially bypass the check. An example can be found in the common vulnerability database, here, if you are curious if this is ever an issue.
You could actually have a vulnerability if you have used the ActionName attribute to map the GET and POST to different methods and the methods have different filters (e.g. POST has the AuthorizeAttribute and GET does not). That would be a pretty serious oversight and would need to be corrected before closing this issue.
On the other hand, this sort of test is likely to produce false positives, especially on pages where the posted content doesn't have an immediate effect on the user experience.
If I came across this report for an MVC site, I would just check to ensure there is a verb restriction on the action method, and then mark the item as "false positive" and move on, without thinking about it too much, for reasons that the OP has explained.
If there isn't a verb restriction, you will either need to add it (with an HttpPostAttribute), or come up with a justification as to why the page/handler is not sensitive or is not less vulnerable when accessed via GET.