I think they mean there's no point taking a single road and making it "nicer" or reducing the traffic on it, without also sorting out other roads in the area (and local transport generally.)
The closure of Loughborough Road failed partly because it led to drivers flooding nearby residential streets trying to pick their way through to Oval/Kennington or wherever. The theory - as practiced and evidenced successfully in the Netherlands and Denmark etc - suggests looking at an area as a whole and dividing the roads into:
1: residential roads (for people to get to where they live)
2: distributor roads (to connect residential roads and main roads) and
3: main roads (for most traffic, travelling longer distances.)
In practice, what this means, is no one should be driving down residential roads unless they live there. Physical infrastructure is used to enforce this - e.g. one way roads, or filters (e.g. a bollard in the middle of the street which allows pedestrians and cyclists through, maintains access for residents, but doesn't allow through traffic.) This then forces through traffic on to "main" roads - which is what they were built for. Coupled with good public transport and good walking/cycling infrastructure, this ultimately reduces motor traffic in the area - and encourages people onto buses/trains/trams and active travel (walking/cycling) because it's quicker.
The Dutch did this - it took them nearly 30 years to build the infra and implement the system - and it works. Few people drive in towns and cities in Holland because it's quicker, easier and safer to cycle or walk. Most kids cycle to school because it's safe.
In practice, what this would mean for the Loughborough Road scheme (for example) is preventing traffic coming into the area from Herne Hill and up Milkwood Road, and from Brixton and up Coldharbour Lane, and onto Loughborough Road. But also creating safe cycle routes and making the trains run, say, every 10 minutes etc etc.
But you also have to do it in all the neighbouring areas as well - Camberwell, Clapham, Dulwish etc. Then the roads are freed up for essential traffic like buses, deliveries, tradespeople and the emergency services.
It's not rocket science and it works in many places around the world, but it takes time and I think at the moment it's a bit too radical for many British people (drivers). It also seems oddly way beyond the comprehension of many who have been sold the 'freedom' of driving, but are still content to spend hours per day sitting in traffic.
