diff --git a/datasette/utils/__init__.py b/datasette/utils/__init__.py
index 5090f67e..69cfa400 100644
--- a/datasette/utils/__init__.py
+++ b/datasette/utils/__init__.py
@@ -884,7 +884,7 @@ def actor_matches_allow(actor, allow):
             values = [values]
         actor_values = actor.get(key)
         if actor_values is None:
-            return False
+            continue
         if not isinstance(actor_values, list):
             actor_values = [actor_values]
         actor_values = set(actor_values)
diff --git a/tests/test_utils.py b/tests/test_utils.py
index d613e999..da1d298b 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -497,6 +497,8 @@ def test_multi_params(data, should_raise):
         ({"id": "garry", "roles": ["staff", "dev"]}, {"roles": ["dev", "otter"]}, True),
         ({"id": "garry", "roles": []}, {"roles": ["staff"]}, False),
         ({"id": "garry"}, {"roles": ["staff"]}, False),
+        # Any single matching key works:
+        ({"id": "root"}, {"bot_id": "my-bot", "id": ["root"]}, True),
     ],
 )
 def test_actor_matches_allow(actor, allow, expected):