diff --git a/packages/mdx/lib/plugin/recma-jsx-rewrite.js b/packages/mdx/lib/plugin/recma-jsx-rewrite.js
index 0858a0be5..1ff7ad0ed 100644
--- a/packages/mdx/lib/plugin/recma-jsx-rewrite.js
+++ b/packages/mdx/lib/plugin/recma-jsx-rewrite.js
@@ -136,12 +136,14 @@ export function recmaJsxRewrite(options = {}) {
             const fullId = ids.join('.')
             const id = name.name
 
-            if (!own.call(fnScope.references, fullId)) {
-              fnScope.references[fullId] = {node, component: true}
-            }
+            if (!inScope(currentScope, id)) {
+              if (!own.call(fnScope.references, fullId)) {
+                fnScope.references[fullId] = {node, component: true}
+              }
 
-            if (!fnScope.objects.includes(id) && !inScope(currentScope, id)) {
-              fnScope.objects.push(id)
+              if (!fnScope.objects.includes(id)) {
+                fnScope.objects.push(id)
+              }
             }
           }
           // `<xml:thing>`.
diff --git a/packages/mdx/test/compile.js b/packages/mdx/test/compile.js
index b98cf6c16..79ef013da 100644
--- a/packages/mdx/test/compile.js
+++ b/packages/mdx/test/compile.js
@@ -504,7 +504,6 @@ test('compile', async () => {
     )
   }
 
-  // TODO: this is incorrect behavior, will be fixed in GH-1986
   try {
     renderToStaticMarkup(
       React.createElement(
@@ -516,27 +515,20 @@ test('compile', async () => {
     const exception = /** @type {Error} */ (error)
     assert.match(
       exception.message,
-      /Expected component `a.b` to be defined/,
+      /^Element type is invalid: .+ undefined/,
       'should throw if a used member is not defined locally'
     )
   }
 
-  // TODO: this is incorrect behavior, will be fixed in GH-1986
-  try {
+  assert.equal(
     renderToStaticMarkup(
       React.createElement(
         await run(compileSync('<a render={(x) => <x.y />} />'))
       )
-    )
-    assert.unreachable()
-  } catch (/** @type {unknown} */ error) {
-    const exception = /** @type {Error} */ (error)
-    assert.match(
-      exception.message,
-      /x is not defined/,
-      'should throw if a used member is not defined locally (JSX in a function)'
-    )
-  }
+    ),
+    '<a></a>',
+    'should render if a used member is defined locally (JSX in a function)'
+  )
 
   try {
     renderToStaticMarkup(