[JENKINS-13536] I think the proper thing to do is to use the Accept header, not the Content-Type header.

core/src/main/java/hudson/model/ParametersDefinitionProperty.java

@@ -148,7 +148,7 @@ public class ParametersDefinitionProperty extends JobProperty<AbstractProject<?,
         Jenkins.getInstance().getQueue().schedule(
                 owner, owner.getDelay(req), new ParametersAction(values), owner.getBuildCause(req));
 
-        if (req.getContentType() != null && req.getContentType().contains("application/json")) {
+        if (requestWantsJson(req)) {
             rsp.setContentType("application/json");
             rsp.serveExposedBean(req, owner, Flavor.JSON);
         } else {
@@ -157,6 +157,12 @@ public class ParametersDefinitionProperty extends JobProperty<AbstractProject<?,
         }
     }
 
+    private boolean requestWantsJson(StaplerRequest req) {
+        String a = req.getHeader("Accept");
+        if (a==null)    return false;
+        return !a.contains("text/html") && a.contains("application/json");
+    }
+
     /**
      * Gets the {@link ParameterDefinition} of the given name, if any.
      */