In 1841 Norhamshire was still a detached part of County Durham.
What I should have said to explain this more fully, is that in 1841 they were shown as born in county, which has been transcribed as born in County Durham.
If they had been born in Norham, born in County Durham would be correct, since until 1844 Norhamshire ( along with Islandshire and Bedlingtonshire) was a detached part of County Durham within Northumberland.