You are correct. It is greener, all other things being equal. E.g. fiber is produced in similar ways.
The 10% instead of the 12.5 percent may be because they include the box and the ream wrappings as part of the total.
But that lower weight comes from somewhere. Usually it would be because the paper is thinner. Thinner paper may be less opaque, which may in turn mean that double sided printing will show through under certain lighting conditions. Thinner paper may require higher quality wood pulp. It may not be strong enough if it uses low grade short fibers, or recycled fibers. Hence my caveat, "All other things being equal"
If the claim is for the same thickness, then the paper density is lower. This implies stiffer cellulose fibers that resist compression better. Not sure how that would be done. Or perhaps they don't squeeze it as hard.
A third possibility: The claim is untrue. Buy a ream and weigh it alongside a ream of the other stuff. Wouldn't be the first time that a marketing 'droid made a claim that he expected no one to actually check. (As in a certain shaving cream that claimed to be able to shave the sand off of sand paper. It did. With a half hour soak.)
Paper is more that just wood pulp. Many papers have small amounts of various minerals (kaolin clay, chalk,...) added. This controls the way ink is absorbed, can add brightness to the paper, and the surface feel. Newsprint is about as close as you come to a pure pulp paper.
It's good that you are skeptical. Steps you can take to check this out:
Weigh the paper. Measure the thickness of the stack.
Ask the maker.
Ask a sales rep of a company that doesn't offer such a product what the downside is of whatever process there competition is using.
I'm sure there is an umbrella organization, something like "International Association of Paper Manufacturers" that may have information about the process being used.
Best: Don't print it. The page you don't use at all is the greenest.
Next: Print using the appropriate paper. Can you use unbleached/recycled paper for internal use or for temporary documents? Note that some papers are not good for printers/photocopiers. Saving a ream of paper that cuts the life of your printer by a year is not a win.
This may mean having multiple printers on your local network with various grades of paper, or alternately having a sophisticated printer with multiple feed trays. These are often not an unreasonable choice for any operation larger than a home office.
80 gram paper that is 30% recycled fiber seems to me to be greener than 70 gram paper that has to be made from all new pulp to be strong enough. (I don't know that this is the case. It's just a possibility.) Much depends on the recycle process compared to the new process.
Next: Use some thought in document layout. With spread sheets I've often found that changing the page orientation, adjusting margins, etc can turn a 20 page document into a 6 page one.
Finally: Do you need to print the whole document? Can you print just a page here and there.