My guess is the damage was caused by the dealers advertisng plate vibrating against the paintwork causing some slight damage, plus it was also trapping rain/wash water for longer than normal at the damaged site. Made worse because hatchback tailgates pick up more than their fair share of gritty, salty road dirt.
If water has penetrated underneath the laquer layer ,or worst still attacked the base colour or primers I think it will only get worse unless its rubbed down to near enough bare metal and the rust treated and relaquered in some way .
On the plus side, rather than having to colour match and blend a large area of metallic paint and laquer You could possibly just paint the affected area, perhaps reproducing the shape of the dealers plate . That way you could use any suitable colour you have to hand,including black .
. If you chose to replace the dealers plate to hide your repairs you could try bending it slightly so it doesnt contact the paintwork , but it might still trap water. Same if you tried padding it with foam sticky trim fixing tape etc.