I think NSE had it spot on south of the Thames with the South Western, South Eastern and South Central Main Lines (although referring to the Great Western as “Thames” and the West Coast and Midland both as “North” is less well thought out).
Brighton is only a little seaside town of no particular importance other than its proximity to London. There are plenty more famous seaside towns that can only dream of having a “Main Line” named after them (Southport, Morecambe, Whitby, Cleethorpes etc) and plenty more with no rail access left at all, so it can think itself lucky it remained so well connected, whatever the LB&SC line is called.
I’m hoping this was said tongue in cheek to ruffle a few feathers. If it was then it clearly worked!!