diff --git a/datasette/views/database.py b/datasette/views/database.py
index 96a58758..e6efddea 100644
--- a/datasette/views/database.py
+++ b/datasette/views/database.py
@@ -612,11 +612,13 @@ class QueryView(View):
                 )
 
         else:
-            await datasette.ensure_permission(
+            visible, private = await datasette.check_visibility(
+                request.actor,
                 action="execute-sql",
                 resource=DatabaseResource(database=database),
-                actor=request.actor,
             )
+            if not visible:
+                raise Forbidden("execute-sql")
 
         # Flattened because of ?sql=&name1=value1&name2=value2 feature
         params = {key: request.args.get(key) for key in request.args}
diff --git a/tests/test_table_api.py b/tests/test_table_api.py
index 388e3979..4ab2f596 100644
--- a/tests/test_table_api.py
+++ b/tests/test_table_api.py
@@ -117,6 +117,29 @@ async def test_query_extras_for_stored_query(ds_client):
     }
 
 
+def test_query_extra_private_for_arbitrary_sql():
+    with make_app_client(config={"allow_sql": {"id": "root"}}) as client:
+        cookies = {"ds_actor": client.actor_cookie({"id": "root"})}
+        response = client.get(
+            "/fixtures/-/query.json?sql=select+1+as+one&_extra=private",
+            cookies=cookies,
+        )
+        assert response.status == 200
+        assert response.json["private"] is True
+        # Anonymous users cannot execute SQL at all here
+        anon = client.get("/fixtures/-/query.json?sql=select+1+as+one")
+        assert anon.status == 403
+
+
+def test_query_extra_private_false_when_sql_is_public():
+    with make_app_client() as client:
+        response = client.get(
+            "/fixtures/-/query.json?sql=select+1+as+one&_extra=private"
+        )
+        assert response.status == 200
+        assert response.json["private"] is False
+
+
 @pytest.mark.asyncio
 async def test_table_shape_objects(ds_client):
     response = await ds_client.get("/fixtures/simple_primary_key.json?_shape=objects")