As long as you are performing the Salifert test correctly (The difference between where the plunger begins and ends is the amount of titrant added), I put all my trust in that test. Alkalinity is a titration by definition, and the Salifert is a titration that is +/- about 0.3 dKH.
I'm not sure why the Hanna may give strange readings. If it matches the Salifert, and you like using it, then great. You could use it as your standard test, then check with the Salifert if you get an unexpected reading.
As for a salt mixing up to an unexpected Alkalinity reading, there could be a few reasons:
It is possible to get a bad batch, but that's pretty unlikely.
I know BRS did a test on buckets of salt being mixed. Whatever their results, the individual components can separate. It's actually pretty amazing to me that a factory can get all that stuff in there somewhat evenly.
Or, as mentioned, make sure your salinity measuring device is calibrated. My opinion is that the best way to do that is by making your own standard with table salt and RODI and adjusting a refractometer to match. If you take a quart jar, put it on a kitchen scale that reads in 0.1 gram increments, zero it out, then add 36.5 grams of table salt by weight, then add 963.5 grams of RODI by weight, then shake it up, you have a full proof seawater standard.
The other way is by messing up the Salifert test somehow.