As the Head Unit has come from another vehicle, the ECU was / is programmed with the configuration from the original donor car and not your car. There can be very subtle differences between the display types and parameters. Although the Head Units are mostly the same between Citroen / Peugeot / DS, each model has a different electronic architecture (CAN system) and of course like the Peugeot, the screen is retractable but is fixed on Citroen like the C5 X7.... Also the dashboard LCD display is different to the Peugeot one - so the parameters are going to be different.
My knowledge covers mainly Citroen systems, so I can't advise you on the exact correct BSI parameters for your 308. But I can almost guarantee you that this is likely to be the problem, which is why I asked if it was original or an upgrade.
The actual ECU is contained in the head unit so some of the options are stored in the memory of the unit - so when the Diagnostic tool is connected, the BSI is reading what is contained in the Head Unit ECU.
The
donor vehicle that the RT6 came from may have significant or even small changes in specification, which may not match your car specification.
I hope that makes sense.
Things to check are Parking Assistance options, Type of Multifunction screen, Type of Dashboard Display, Directional Lighting. I the Audio / Head Unit / RNEG2 ECU, check the number of aerials are correct, the dual tuner options are set right etc. BUT be VERY Careful here - please don't guess at the options, because one simple change with the wrong option can leave the car inoperable or cause all sort of problems.
Sometimes there may be options that may seem like they should be changed, but you must not change any values that have DEFAULT values (the BSI technical programming document will state this that the dealer has access to) - as the same BSIs are used in several cars and have to be able to allow for the different car designs. Things like the temperature info, A/C settings and how / where they are displayed are very important to be set correct.
I hope you appreciate I can't go into specifics for your car as they will be different for the Peugeot. The dealer should be able to check this for you if they have experience of this -
but in any case, they should have the correct BSI technical document for the 308 they can run through that tells them what the options should be set to for the RT6. 
