The lack of this was incredibly disappointing for me. The background war table mission should have eventually awarded a background specific armour/armour schematic.
I think what bugs me more is that the memories reflect whatever armor your Inquisitor is currently equipped with, which totally screws with the continuity.
Eh, this is pretty easy for me to headcannon away. The Inquisitor isn't watching the memories as if they were recorded and uploaded to youtube. They are having them dumped into their brain.
The human brain cheats all the time, essentially fabricating details from other details. When the memory gets popped back into their brain, that is what happens. The broad stuff is accurate, but details like what they were wearing is edited. When the Inquisitor thinks of their armour, they don't picture that ratty old set they sold off last year. They think of the awesome new set they have been wearing for months now.