That is incorrect. The gunsmith part of that video had no weapons ready for reforging. The stuff under the packages were Miscellaneous items (boosters, etc).
It doesn't appear any of the new weapons will allow for reforging based on what we've seen so far. The weapons now have more options that can be selected to fine tune it how you wish (with limitations of course). In their eyes I think reforging was a mistake. Everyone just opted for the "god rolls" yielding the same weapon had by everyone.
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Sorry, my information was incorrect, it's under the miscellaneous category. If you go to 53 minutes and 30 seconds you can see where it says reforge weapons.
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You're right I see it. It's probably just around for the older weapons. None of the legendaries they pulled up had the reforge icon. When the second guy right after picked up his weapon from the weapon smith, the gunsmith didn't even say reforge (just had the "refresh" timer under Misc. I dunno. Guess we'll see.