No you are not wrong, she does not have enough backing.
Converting the 2 meters to inches (I rounded at 39" per meter) + the 5" she has a total length of 83" (plus about a half inch given my rough and tumble conversion). If she cuts that in half she will have two pieces of fabric measuring 41.5 x 43. No matter which way she sews these two pieces together she will be short.
I just tried it using an online calculator for the diagonal method and she is way short there too.
http://www.multi-patch.com/html/fabric_calc.php
She will need to get more fabric and add an additional seam to her backing or get all new backing with an absolute minimum of 4.25 yards (or 4 meters which will give you the extra you prefer to have as well) The extra fabric will be for you to test tension on the sides and attach to your leaders. She will have extra to add to her stash once she cuts it off after quilting. Might even be enough to do the binding.
PS I suspect the LQS forgot to double the length of fabric which is what is needed to get the 43" wide fabric to be wide enough. Had she bought wide back fabric (108" wide) 2 meters would have been ample. If she doesn't believe you, tell her to go back to the shop she bought the fabric from and have them explain exactly how to cut and piece her 2 meter x 45" WOF to back a quilt that measures 66" x 77"