Bedfordshire Boy, Chempat and Jaywit have just expressed exactly what I was thinking in response to the ponts you raised. I'm afraid that I think you have it wrong on so many levels.
I don't know where you get your information from but I think you have been misled.
I will pick up on a coupe of points which I find incredulous:
there are no numbers for the rates of illegitimacy several hundred years ago, and just because someone was named as father on a birth certificate or baptism register, or just because the parents were married, it does not necessarily follow that the child belongs to that man/ husband. If you think illegitimacies were rare, you are kidding yourself.
What punishments/ penalties did girls who 'strayed' have to endure that made illegitimacies so rare?
Why on earth would a Spencer group administrator be unwilling to admit that some Spencers in the dim and distant past did not hold the surname Spencer? That sounds completely illogical. I simply do not get this. Why on earth would it matter let alone be something to be secretive about? I believe there are specific requirements to being DNA project administrators and I think this particular one may need to be reported.
I think if you are searching for the truth and seriously trying to trace English Spencers, then you might need to do a bit of serious reading about history, origins of surnames and genealogy in general. For a start I can recommend Ancestral Trails by Mark Herber and Early Modern Genealogy by Paul Chambers, and I'm sure there are many many more.
I hope this doesn't come across as too harsh, but it is just meant as a bit of advice which you can take, or not, as you wish.
You will note that everyone who has replied to your threads is slightly critical of some of your claims, so I think some alarm bells should be ringing. Many of these people are respected and experienced researchers, so it may be worth considering their advice and comments.