Please don’t tamper with the permissions of your Time Machine backup as this could indeed get you into trouble.
One of the problems you have trying to copy your Time Machine backup is the fact that Time Machine uses a feature called “hard links” which lets a single file show up in different folders multiple times. I. e., the file (precisely: its inode) is stored only once but it can have an arbitrary number of associated directory entries. If you copied these files using a tool unaware of hard links you would probably create unnecessary duplicates of these hard-linked files.
You should use Disk Utility (found in /Applications/Utilities) to clone the whole backup partition to the new drive or partition. Doing so will get you around the hard link problem as a block-level copy will be made instead of a file-level copy.