Yes, this fix is easier.

lexer/smarty_internal_templateparser.y

@@ -785,9 +785,11 @@ value(res)       ::= ns1(c)DOUBLECOLON static_class_access(s). {
         if (isset($this->smarty->registered_classes[c])) {
             res = $this->smarty->registered_classes[c].'::'.s[0].s[1];
         } else {
-            trigger_error('Using unregistered static method "' . c.'::'.s[0] . '" in a template is deprecated and will be ' .
-                    'removed in a future release. Use Smarty::registerClass to explicitly register ' .
-                    'a class for access.', E_USER_DEPRECATED);
+            if (s[2] === 'method') {
+                trigger_error('Using unregistered static method "' . c.'::'.s[0] . '" in a template is deprecated and will be ' .
+                        'removed in a future release. Use Smarty::registerClass to explicitly register ' .
+                        'a class for access.', E_USER_DEPRECATED);
+            }
             res = c.'::'.s[0].s[1];
         } 
     } else {
@@ -1123,7 +1125,7 @@ static_class_access(res)       ::= method(m) objectchain(oc). {
 
                   // static class constant
 static_class_access(res)       ::= ID(v). {
-    res = array(v, '');
+    res = array(v, '', 'constant');
 }
 
                   // static class variables

tests/UnitTests/TemplateSource/ValueTests/PHPfunctions/PhpFunctionTest.php

@@ -255,8 +255,9 @@ class PhpFunctionTest extends PHPUnit_Smarty
 		}
 
 		if ($shouldTriggerDeprecationNotice) {
-			$this->assertStringContainsString('Using unregistered function', $errorMessage);
+			$this->assertStringContainsString('Using unregistered ', $errorMessage);
 		} else {
+			$this->assertEquals('', $errorMessage);
 			$this->assertEquals($expected, $output);
 			$this->assertEquals('', $errorMessage);
 		}
@@ -295,6 +296,9 @@ class PhpFunctionTest extends PHPUnit_Smarty
 			['{$a|addslashes}', '', true],
 			['{$a|sha1}', '', true],
 			['{$a|get_parent_class}', '', true],
+
+			['{StaticMethodsTesterClass::giveMeEmptyString($a)}', '', true],
+			['{StaticMethodsTesterClass::EMPTY_STRING}', '', false],
 		];
 	}
 
@@ -326,3 +330,12 @@ class TestIsset {
         return $v;
     }
 }
+
+class StaticMethodsTesterClass {
+
+	const EMPTY_STRING = '';
+
+	public static function giveMeEmptyString($data) {
+		return '';
+	}
+}