Are there any genuine friendship sites?I don't know. Depends on how you define a "genuine friendship site". In any case, I really would advise a real world meeting and making (?) of a friendship. I like texting, sure, but I'm more of an advocate for forming friendships in real life.
Other than that, there are websites and apps such as Badoo (which is a dating site as well i guess) and random chat sites, where, if you're inclined to and are lucky enough and are genuinely interested in having a conversation and a friend, you can form the same. But, as already stated by Hari Gopal Reddy, these things come with a "Beware" warning. You might find content which you may be offensive and chances are that people who usually stick around such sites are not their for forming friendships.
So I would recommend apps and sites which have to be linked to any of your social network accounts, because, quite frankly, anonymity does tend to bring out the worst in a lot of people. It shouldn't, but it does.