diff --git a/packages/mdx/lib/plugin/recma-jsx-rewrite.js b/packages/mdx/lib/plugin/recma-jsx-rewrite.js
index 0858a0be5..e1d8dbf50 100644
--- a/packages/mdx/lib/plugin/recma-jsx-rewrite.js
+++ b/packages/mdx/lib/plugin/recma-jsx-rewrite.js
@@ -136,11 +136,25 @@ export function recmaJsxRewrite(options = {}) {
             const fullId = ids.join('.')
             const id = name.name
 
+            const isInScope = inScope(currentScope, id)
+
             if (!own.call(fnScope.references, fullId)) {
-              fnScope.references[fullId] = {node, component: true}
+              const parentScope = /** @type {Scope|null} */ (
+                currentScope.parent
+              )
+              if (
+                !isInScope ||
+                // If the parent scope is `_createMdxContent`, then this
+                // references a component we can add a check statement for.
+                (parentScope &&
+                  parentScope.node.type === 'FunctionDeclaration' &&
+                  isNamedFunction(parentScope.node, '_createMdxContent'))
+              ) {
+                fnScope.references[fullId] = {node, component: true}
+              }
             }
 
-            if (!fnScope.objects.includes(id) && !inScope(currentScope, id)) {
+            if (!fnScope.objects.includes(id) && !isInScope) {
               fnScope.objects.push(id)
             }
           }
diff --git a/packages/mdx/test/compile.js b/packages/mdx/test/compile.js
index b98cf6c16..70db8b800 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(
@@ -521,11 +520,10 @@ test('compile', async () => {
     )
   }
 
-  // TODO: this is incorrect behavior, will be fixed in GH-1986
   try {
     renderToStaticMarkup(
       React.createElement(
-        await run(compileSync('<a render={(x) => <x.y />} />'))
+        await run(compileSync('<a render={() => <x.y />} />'))
       )
     )
     assert.unreachable()
@@ -533,11 +531,21 @@ test('compile', async () => {
     const exception = /** @type {Error} */ (error)
     assert.match(
       exception.message,
-      /x is not defined/,
+      /Expected object `x` to be defined/,
       'should throw if a used member is not defined locally (JSX in a function)'
     )
   }
 
+  assert.equal(
+    renderToStaticMarkup(
+      React.createElement(
+        await run(compileSync('<a render={(x) => <x.y />} />'))
+      )
+    ),
+    '<a></a>',
+    'should render if a used member is defined locally (JSX in a function)'
+  )
+
   try {
     renderToStaticMarkup(
       React.createElement(await run(compileSync('<X />', {development: true})))