@The Internet Dick @AnOminous This is a puzzler to be sure. I kinda think you're both half right. I think it's complicated and has probably even been made into several psychological studies by now - but I can't be arsed to go looking for them.
I think a friend is someone who you develop a family-like attachment with but who isn't genetically linked to you (however family members can also be friends); it's a platonic love for another human being, who you want to share your company with but whom you don't wanna fuck. That's a friend.
Whether you meet someone online and exchange emails and social media to stay in touch; or met someone in a pub who you strike up a conversation, form a rapport with and socialise whenever you see each other in that pub - it's kinda the same sort of amicable acquaintance. Your relationship is limited by a specific set of conditions (either the Internet or the pub) so it's a shallow friendship. But it's still one that can be developed further if both parties are willing to put in the extra effort.
You
could invite your pub-mate over to drink at your house instead of just the pub or go see a game with you. And you
could invite your Internet fwen to meet irl at a convention or stay at your home if they're ever in the country. Internet fwens are basically just the pen-pals of the modern era. It's not something new; just the way that pen-pal is discovered is "new"
Tl:dr Internet frens are on the same level as irl acquaintances and can also be developed into full friendships if both parties are so inclined. Ergo: you're both kinda right.