diff --git a/numpydoc/tests/test_validate.py b/numpydoc/tests/test_validate.py
index f3be498b..910c1a1d 100644
--- a/numpydoc/tests/test_validate.py
+++ b/numpydoc/tests/test_validate.py
@@ -1576,10 +1576,7 @@ def test_bad_generic_functions(self, capsys, func):
             (
                 "BadSummaries",
                 "wrong_line",
-                (
-                    "should start in the line immediately after the opening quotes",
-                    "should be placed in the line after the last text",
-                ),
+                ("should be placed in the line after the last text",),
             ),
             ("BadSummaries", "no_punctuation", ("Summary does not end with a period",)),
             (
diff --git a/numpydoc/validate.py b/numpydoc/validate.py
index 235841ea..2c8c9253 100644
--- a/numpydoc/validate.py
+++ b/numpydoc/validate.py
@@ -44,9 +44,8 @@
 # modify/remove
 # start-err-msg
 ERROR_MSGS = {
-    "GL01": "Docstring text (summary) should start in the line immediately "
-    "after the opening quotes (not in the same line, or leaving a "
-    "blank line in between)",
+    "GL01": "Docstring text (summary) should start right after, or on the "
+    "line following the opening quotes",
     "GL02": "Closing quotes should be placed in the line after the last text "
     "in the docstring (do not close the quotes in the same line as "
     "the text, or leave a blank line between the last text and the "
@@ -347,6 +346,7 @@ def start_blank_lines(self):
             for i, row in enumerate(self.raw_doc.split("\n")):
                 if row.strip():
                     break
+
         return i
 
     @property
@@ -708,7 +708,7 @@ def validate(obj_name, validator_cls=None, **validator_kwargs):
             "examples_errors": "",
         }
 
-    if doc.start_blank_lines != 1 and "\n" in doc.raw_doc:
+    if doc.start_blank_lines not in (0, 1) and "\n" in doc.raw_doc:
         errs.append(error("GL01"))
     if doc.end_blank_lines != 1 and "\n" in doc.raw_doc:
         errs.append(error("GL02"))