I just tried this using the tubes from 3 different API kits and the syringe from a Salifert kit and can't agree with you.
Once the test tube is wet (API does suggest rinsing the tube before you run the test) it does tend to make the water level slightly higher.
On the dry tubes taking the concave meniscus into account, the tubes did measure to 5 ml as expected.
Most of these kits are created assuming a small degree of user error. Between the 'flat spoon of powder' to 'is that still purple or is it really blue now?'
Since API does not include a syringe in their kits, filling it so the bottom of the meniscus is at the top of the line on the test tube, should give you an accurate reading