What you may be failing to notice is that most mesh determiners have several graphs for mesh, the AWT tool most commonly used has a large area that many printers use...wrongly, as its meant for MULTI-filament mesh and its not likely that you are using a multi-filament mesh so if that is what your using you will of course get an incorrect reading.
That all said, you are correct that a mesh tool has no regard for thread diameters. Its a simple interference pattern that uses a moire effect as a tool rather than that nasty problem we associate it with in printing.
One aspect that you should look at is that all (quality) mesh will have the mesh's information printed on the sewn edges on one side of the fabric. It would typically include the thread count in both US & metric, the thread diameter and the manufacturers name. Typically this information is printed almost every meter or so..if your mesh does not have this information than its dubious as to both the stated mesh count and certainly its quality. I would ask your supplier to provide a photo of the bolt of mesh with those details.
Lastly, its possible that you were indeed shipped the wrong mesh. Maybe not a 110, but maybe something altogether wrong compared to what you were expecting. Curiously, what brand of mesh was stated by your supplier?