Thought I would chime in. And hopefully I will not offend, but I think that maybe some people are thinking this, but don't want to say what I am going to say.
I don't think it is appropriate to nurse an 11 yo. There are major developmental differences between a 3 yo (or even a 7 yo) and an almost teenager. Puberty, even in boys this age, is already beginning or is in full force. I just don't see it as being a developmentally appropriate activity to be encouraging on the part of the mother and I cannot fathom an otherwise developmentally normal child of that age wanting to or needing to "nub".
If this case is true, which I have doubts about, than there are other issues going on and I do believe that this could have other long term phychological ramifications, especially if the child finds out later (if he doesn't already know) that he and his mother were engaged in what can easily be construed by others in our society, as a socially and sexually deviate activity.
Now to my more controversial thoughts:
To the arguement that breasts are not inherantly sexual, I disagree. I view breasts as a multi-purpose "organ". Yes, breasts are primarily for feeding children...that is why they make milk. But breasts are complex in their phsiological make-up and breast-feeding by it evolutionary and biological nature is usually an enjoyable and often sensual experience. It feels good. There is a biological purpose for that in that it allows us to have a bonding and intimate relationship with our children (and therefore will encourage us to protect and nuture them, which allows for the propogation of our species). Sensuality and sexuality are very closely linked and are often difficult to distiguish from one another...I think that is why our society in general is so weird about breastfeeding beyond infancy. I wholeheartedly disagree that if we enjoy breastfeeding then that means it is "wrong". I EBF both of my children. But there comes a natural end to this developmental stage of childrearing and IMO, this pair is LONG past their "expiration" date.
To put it bluntly, we release hormones when we nurse our children that provide us with a physical "payoff" (sense of calm, relaxation, love) and in many people the potential for sexual arousal. I certainly am able to get sexual enjoyment from breast stimulation by my partner that I just don't get from getting my feet rubbed (without getting to graphic, yes it can take me all the way). And I don't think it is "all in my head" (i.e. that because our brains are our primary sexual organ that I can convince myself that it is pleasurable and therefore can "preform").
She may not have milk any more, but she certainly could be benefiting from the hormonal release that comes with the physical act of putting breast to mouth. That, in my opinion is not appropriate when we are dealing with a child entering their second decade of life and into their own blossoming sexuality.
IMO, like anything else that involves sensuality and intamacy, breastfeeding/nurturing CAN be sexual and CAN be used as a form of abuse, whether intentionally or unintentionally (I don't want to believe that this mother is intentionally hurting her child). And I also take exception to the premise that you cannot "force" a child to breastfeed/nurture. How is it different than coersing a child to be sexually/sensually intimate in other ways (at least in theory)? I think that the young men abused by some priests over the course of the last 1/2 century (and longer) would disagree that you cannot be coerced or forced to do things you don't want to do, ESPECIALLY by people in the position of power/authority/or love.
This case, if true, just leads me to wonder what the long term ramifications will be for this child and his relationship with his mother and other people he may choose to be intimate with later in life, as I do not view it as a healthy and age/developmentally appropriate activity and could potentially be very harmful...