Writers always lie. Look how much Bendis lies in interviews.
Kobik didn’t implant any false memories on Steve though and Spencer mentions that in his latest interview
Kobik didn’t implant anything, she rewrote reality to her whims, she’s a cosmic cube and she has the power to do that.
Steve is a member of Hydra, a child’s idealized version Hydra but a member of Hydra nonetheless, which is what makes this thing even more wrong.