Read this part carefully.
"The following center-fire cartridges may be used, along with others not identified in this list that meet the straight-walled cartridge criteria in the next section below".
I read that to say, this list is okay as written. Whether or not the cartridges pass the below criteria, this list is approved. You may also use any other cartridges NOT included in this pre-approved list as long as they meet the following criteria. So yes to answer the question, I believe the .45-70 is okay.