Cowering and Rolling over

Ok so this isn't about Bane, just curious about the pup down the road.
She is a gorgeous Dog de Bordeaux cross and is a month or so younger than Bane (maybe 5 months?) and about twice the size!
She is very friendly and whenever I see her I always try to make a fuss. The thing is when I bend down to stroke her, she immediately lays down and cowers and most of the time will roll over. When doing this, her owner will quite often tell her off and try to pull her up off the floor. Bane has met her a few times and she does the same, she cowers and rolls over. I don't think she really has any interaction with other dogs but was just wondering if there is any reason why she does it so often.
Are some dogs just quite scared and submissive naturally? Or is it more of a case that she has been made that way by how her owner has raised/disciplined her?

Maybe she is just like it outside in the big wide world. It could be over discipline, but not sure how you will know which really. How does the owner tell her off?

Yeah was just wonderin if some pups are more cautious of the outside world than others
He will just shout 'Roxy NO, get up!' Over and over and sort of drag her away...would like to see him try when she is fully grown :p

I'd imagine a combination of a naturally timid personality as as Sue has said, over discipline. Sounds like a mismatched ownership, hate seeing shy dogs being shouted at She would get up when he was comfortable with patience and confidence building techniques.

Yeah he doesn't seem to be particularly patient with her as she is doing what comes naturally to her, but then getting told off for it. Really wana knock on and see if he wants to take her to the park with me and Bane one day for a play but he seems a little odd!  

Aww poor girl a

Poor dog   

You just want to cuddle and love the dog.

She is such a big softie would make a great snuggly teddy bear