This isn't about me or DH, and it's long, so bear with me. 

I have a friend from HS (I'll call her Jane) who had a child with a college boyfriend.  Child is almost 10.  Jane was still together with BF at the time the child was born, but they lived 1000 miles apart after BF's mom, with whom they had been living, told Jane she should go live with her own parents.  I.e., she kicked her out about 6 weeks before the baby was born, and BF did not come with her.  BF was present for the birth but did not sign the birth certificate or any acknowledgement of paternity at the hospital.  He saw his son again when the baby was a month old.  About a month after that, BF and Jane broke up.  She has not seen or heard from BF since, and BF has not seen the child since that 2 day visit when he was 1 month old.   

Up until very recently, child had no clue who his father was and never expressed any curiosity.   His maternal grandfather was his father figure.  BF has never paid or offered child support, nor has Jane asked him for it.  The child is supported by and currently lives with Jane's parents, who also do a lot of the child care while Jane is in school and/or at work.  Jane's parents are wealthy and have no problem supporting Jane and her child.  Jane has had some minimal contact with BF's parents, who have sent a birthday gift for the child every year and occasionally ask for pictures, which she sends.  

A couple months ago the paternal grandparents asked to come see the child (first time since he was a month old), and Jane agreed.  They came and I guess had a nice visit.  Since then, they've been texting and video chatting with the child (he has his own phone).  About a week ago, BF started texting the child.  He apparently told the child the reason he hadn't seen him in all these years was that Jane's parents had prevented it (not true, although they were not unhappy he was out of the picture).  He also told the child he wasn't ready to see him yet, but would be in a year.  (WTF??)  Jane's parents and siblings told her that she should block him from the child's phone or at least try to control what the child sees, since BF is lying to him.  Jane said she's not worried about BF, because there's no way he'd be able to get any custody or visitation.

Her parents and siblings, and I also, told her that if he tries to get visitation, he'll get something - probably some kind of step up plan eventually leading to long distance visitation.  She can't believe this is possible.  I really have no experience with a situation like this, as my DH has a court order and has had 50/50 custody of his kids since he and BM split, but I've heard and read enough to think that Jane is misinformed.  She claims a lawyer told her this almost 10 years ago when she consulted him before the child was born, but her parents remember nothing of the sort.  Do any Step-Talkers have familiarity with a situation like this?  Are we wrong in thinking BF can get some kind of visitation if he decides to prove his paternity and seek it, even though he's been a total deadbeat  for almost ten years?