Don't bring up authorization just because group ID doesn't match

Sparkle/SUFileManager.h

@@ -103,6 +103,7 @@ NS_ASSUME_NONNULL_BEGIN
  * If the owner and group IDs match on the root items of targetURL and matchURL, this method stops and assumes that nothing needs to be done.
  * Otherwise this method recursively changes the IDs if the target is a directory. If an item in the directory is encountered that is unable to be changed,
  * then this method stops and returns NO.
+ * While this method will try to change the group ID, being unable to change the group ID does not result in a failure if the owner ID can be changed or matched.
  *
  * This is not an atomic operation.
  */

Sparkle/SUFileManager.m

@@ -434,15 +434,30 @@ - (BOOL)changeOwnerAndGroupOfItemAtRootURL:(NSURL *)targetURL toMatchURL:(NSURL
         // Speeds up the common case
         return YES;
     }
-
-    if (![self _changeOwnerAndGroupOfItemAtURL:targetURL ownerID:ownerID groupID:groupID error:error]) {
-        return NO;
+
+    // If we can't change both the new owner & group, try to only change the owner
+    // If this works, this is sufficient enough for performing the update
+    NSNumber *groupIDToUse;
+    if (![self _changeOwnerAndGroupOfItemAtURL:targetURL ownerID:ownerID groupID:groupID error:NULL]) {
+        if ((targetOwnerID != nil && [ownerID isEqualToNumber:targetOwnerID])) {
+            // Assume they're the same even if we don't check every file recursively
+            // Speeds up the common case like above
+            return YES;
+        }
+
+        if (![self _changeOwnerAndGroupOfItemAtURL:targetURL ownerID:ownerID groupID:targetGroupID error:error]) {
+            return NO;
+        }
+
+        groupIDToUse = targetGroupID;
+    } else {
+        groupIDToUse = groupID;
     }
 
     if (isTargetADirectory) {
         NSDirectoryEnumerator *directoryEnumerator = [_fileManager enumeratorAtURL:targetURL includingPropertiesForKeys:nil options:(NSDirectoryEnumerationOptions)0 errorHandler:nil];
         for (NSURL *url in directoryEnumerator) {
-            if (![self _changeOwnerAndGroupOfItemAtURL:url ownerID:ownerID groupID:groupID error:error]) {
+            if (![self _changeOwnerAndGroupOfItemAtURL:url ownerID:ownerID groupID:groupIDToUse error:error]) {
                 return NO;
             }
         }