diff --git a/src/client/auth.test.ts b/src/client/auth.test.ts
index 1a6ef5af..daa98de5 100644
--- a/src/client/auth.test.ts
+++ b/src/client/auth.test.ts
@@ -60,16 +60,18 @@ describe("OAuth Authorization", () => {
       // Verify second call was made without header
       expect(mockFetch).toHaveBeenCalledTimes(2);
       const secondCallOptions = mockFetch.mock.calls[1][1];
-      expect(secondCallOptions).toBeUndefined(); // No options means no headers
+      // The second call still has options but doesn't include MCP-Protocol-Version header
+      expect(secondCallOptions).toBeDefined();
+      expect(secondCallOptions?.headers).toBeUndefined();
     });
 
-    it("returns undefined when all fetch attempts fail", async () => {
+    it("throws an error when all fetch attempts fail", async () => {
       // Both requests fail
       mockFetch.mockRejectedValueOnce(new Error("Network error"));
       mockFetch.mockRejectedValueOnce(new Error("Network error"));
 
-      const metadata = await discoverOAuthMetadata("https://auth.example.com");
-      expect(metadata).toBeUndefined();
+      await expect(discoverOAuthMetadata("https://auth.example.com"))
+        .rejects.toThrow("Network error");
       expect(mockFetch).toHaveBeenCalledTimes(2);
     });
 
diff --git a/src/server/auth/handlers/register.ts b/src/server/auth/handlers/register.ts
index 2a74b4a4..30b7cdf8 100644
--- a/src/server/auth/handlers/register.ts
+++ b/src/server/auth/handlers/register.ts
@@ -75,13 +75,13 @@ export function clientRegistrationHandler({
       }
 
       const clientMetadata = parseResult.data;
-      const isPublicClient = clientMetadata.token_endpoint_auth_method !== 'none'
+      const isPublicClient = clientMetadata.token_endpoint_auth_method === 'none'
 
       // Generate client credentials
       const clientId = crypto.randomUUID();
       const clientSecret = isPublicClient
-        ? crypto.randomBytes(32).toString('hex')
-        : undefined;
+        ? undefined
+        : crypto.randomBytes(32).toString('hex');
       const clientIdIssuedAt = Math.floor(Date.now() / 1000);
 
       // Calculate client secret expiry time