No you are correct. When the Professional game came too NE , Durham joined the cricket elite they used to play around the old county boundaries eg Durham City, Stockton on Tees , Darlington, Hartlepool, Ashbrooke, Gateshead Fell. As Northumberland never played in the County Championship and played mainly in the industrial south east of the county eg South Northumberland C C . Sponsorship was needed at Durham and Tyneside quickly jumped on the bandwagon with Scottish and Newcastle Breweries becoming prominent. Soon after odd games were played 'over the border' to give them a taste of the professional game.Since the new ground at Chester le Street, on the banks of the River Wear was opened it was adorned with the Newcastle Breweries adverts. Sunderland and Vaux were slow to respond, mainly due to lowly position financially of the football club and the outcome of Swallow Hotels decision to close the brewery.This is how the Newcastle link got a foothold. In the old days in the 1960's, Colin Milburn era, Co Durham was Co Durham and Sunderland was the county team, football wise.
Traditionally the Sunderland fan base in the south and north west of Co Durham was loyal to SAFC. Ask the older generation, two that I know of told me 3 full coaches went every hiome game to Roker Park from Esh Winning in 1960's and one to Newcastle. Six coaches would leave from Consett to Roker every game. The biggest SAFCSA branch outside the main branch in Sunderland was the Consett / Stanley branch. Those people strongly thought that Sunderland was Co Durham's club and still do.