One of her cousins knew that her own father was illegitimate but said that Clarence, Una's father, was definitely ("Oh, definitely!") Arthur's son with Annie before they got married; and Una said she could "see" her father in Arthur.
I don't see what was definite about it at all.
Clarence's middle name is Watson, and that's a bit of red flag to me for him being Arthur Stubbs' son. It was quite usual for an unmarried mother to give her child a name referencing the father, even if he couldn't be named officially on the birth certificate. Just because Arthur and Annie lived opposite each other in the same street and Clarence was born at Arthur's house, doesn't actually make Arthur the father. If he was, would it have been so unusual to have his name on the birth certificate? and if Arthur was Clarence's father, why didn't they marry before he was born?
I appreciate we'll never know, but I felt that this bit was skated over a bit too easily.