I’m not entirely sure how weapon rarity works, but what I think shouldn’t be the case is that the display of hero stats changes if you equip a higher-rarity weapon even if that weapon isn’t active. So for example, I have base +0 % Fire Rate, but when I equip a rare Firelance, the stats change to +20 % Fire Rate, which gets also displayed if I switch to my other weapon, a common Railgun. However, that fire rate bonus is not applied to the Railgun (and it shouldn’t be).

EDIT: Equipping a common Torchlight, for example, also displays a +15 % Damage Bonus that has no effect on your other weapon.

EDIT2: If you select your other weapon in the hero overview screen, the stats don’t change. If you switch your active weapon properly in the game and then open the hero screen, the changed stats are displayed properly.

It’s very confusing nonetheless if some weapons have built-in damage / fire rate bonuses because the weapon info card doesn’t indicate that anywhere. It’s redundant to display any stat bonuses that are only applicable to that weapon because the weapon info card displays all the resulting numbers. The hero stats on the left I would expect to be true regardless as to which weapon is active.