Reworked this change a bit.

- GHApiInfo need not be public because it's not publicly exposed.
- Throwing an exception is better IMO as it allows richer error message,
  including the differentiation between unreachable host name vs wrong
  URL, and reporting the API endpoint URL that was actually tried.

src/main/java/org/kohsuke/github/GitHub.java

@@ -455,21 +455,27 @@ public boolean isCredentialValid() throws IOException {
         }
     }
 
+    private static class GHApiInfo {
+        private String rate_limit_url;
+
+        void check(String apiUrl) throws IOException {
+            if (rate_limit_url==null)
+                throw new IOException(apiUrl+" doesn't look like GitHub API URL");
+
+            // make sure that the URL is legitimate
+            new URL(rate_limit_url);
+        }
+    }
+
     /**
      * Ensures that the API URL is valid.
+     *
+     * <p>
+     * This method returns normally if the endpoint is reachable and verified to be GitHub API URL.
+     * Otherwise this method throws {@link IOException} to indicate the problem.
      */
-    public boolean isApiUrlValid() throws IOException {
-        try {
-            GHApiInfo apiInfo = retrieve().to("/", GHApiInfo.class);
-            try {
-                new URL(apiInfo.getRateLimitUrl());
-                return true;
-            } catch (MalformedURLException mue) {
-                return false;
-            }
-        } catch (IOException e) {
-            return false;
-        }
+    public void checkApiUrlValidity() throws IOException {
+        retrieve().to("/", GHApiInfo.class).check(apiUrl);
     }
 
     /**

src/test/java/org/kohsuke/github/GitHubTest.java

@@ -124,6 +124,6 @@ public void testGitHubEnterpriseDoesNotHaveRateLimit() throws IOException {
     @Test
     public void testGitHubIsApiUrlValid() throws IOException {
         GitHub github = GitHub.connectAnonymously();
-        assertTrue(github.isApiUrlValid());
+        github.checkApiUrlValidity();
     }
 }