The speculation re: Gordon and Welker comes from the fact that their specific infractions are being punished differently under the new rules than the old ones. The new threshold for positive weed tests will increase from 15 nanograms per mL to 50 (the same threshold as baseball players and air traffic controllers, and 1/3rd the threshold of Olympic athletes). Since Gordon flunked for having 16 nanograms per mL, his fail would be a clear pass under the rules.
Similarly, under the new policy amphetamines will no longer be a PED (four-game suspension on first offense) and instead will fall under the drug abuse police (enter their substance abuse program as a first offense, no suspension).
Basically, it's not just an amnesty for past infractions: it's applying the new rules to past infractions, and erasing them if they no longer qualify. I may be mistaken, but even if they do that, I don't think it'll do anything for Browner or Tyms, since the punishments for their infractions won't be changing IIRC.
Considering that Browner's suspension apparently stems from failing a weed test (somehting I didn't realize until just now:
http://nesn.com/2014/03/brandon-browners-four-game-suspension-stems-from-missing-drug-tests/), it could all come down to whether A) his positive weed test was over or under the new threshold, or B) whether the new policy changes its stance on missing drug tests while out of the NFL.