Why would staff have to accompany anyone over the bridge?
Just find some common decency (and sense) leave the gates open- people can bleep their Oyster cards and pedestrians can use the bridge. I'm sure 99.9% of people can be trusted, despite the low opinion if people on here.
The train company's refusal is selfish, unimaginative, and frankly cruel.
If they had a iota of goodwill towards the people of forest hill (and give themselves some good PR, they'd allow use of the bridge