Definitely don't take them down. As others have said, privacy settings exist for a reason and she can use them. I would personally reply to her boyfriend and not reach out to Sam, as there's a chance she had no idea he sent that message. I love /u/mm172's suggested reply here--you're offering to help on your end, suggesting something that might help Sam, and gently letting him know you're not giving into this (really bizarre) request.
If it makes you feel any better, I can relate to this from Sam's perspective. My ex best friend (ex friend for other reasons, not due to jealousy) is living my dream life. She went to my dream school and has my dream career. She travels all over the world. She has pretty much unlimited financial resources to do this and to continue her education.
I was doing very well academically while working extremely hard to survive financially. Then I found out I have a severe, chronic medical condition that means all of that is out the window. Period. I had to leave school toward the end of undergrad. Even if I am able to return to school eventually, I can never go into that field. I was always happy for her when we were friends even though it was hard for me to see. It's even harder now, especially since I don't even like the woman. But that's not her problem at all and she deserves to be able to share her happiness on social media!
I've learned to stop torturing myself by looking at photos of her doing all the things I can never do because that's completely on me. You're not uploading photos of yourself, tagging Sam, and captioning them with "don't you wish you looked like this!?" Obviously that would be different. You're doing nothing wrong here and no one has the right to put any impetus on you for Sam's issues.
I would never want my former friend to know how I used to feel about seeing her photos. That would be fucking humiliating. I would be furious if anyone else tried to talk to her about it on my behalf. I really suggest not confronting Sam with this--she could very well be dealing with it privately like I did, and her boyfriend decided to pull an idiot move. If you find out later that it was at her request, then address it with her directly, but until then there's no need to make her feel even worse about her situation.