I run fish only set up at 1.016-1.018 it realy seems to reduce stress on the fish. in a reef that does not apply since all the worlds oceans with few exceptions eg. dead sea (not including unnatural polutants) have basically the same chemistry and SG at 1.025 most of the more delicate reef specimines require a SG of atleast 1.020 minimum and prefer the more natural 1.024-1.025
back to your problem; I think your measuring equipment should be suspect. fact is the salt is being added so the SG is definitly going up, your equipment just isn't measuring it accuratly. the moving parts in some tools will "gum" up sometimes, for example.
ease off on the salt until you get another opinion, like a new tool. your SG could be at 1.030 or higher, plus the salt takes time to disolve in the water and dissapapate so it will register on a tool.
I see above your getting a refractometer, you can obtain a good quality one at most pet stores for under $10 those are the most accurate since theres no moving parts. don't get a plastic one it's tempting sometimes to get a fancy plastic "doodad" but you realy don't need it. the simple glass unit works the best. no beads no arms or anything.