Alice, I am sorry if you came across any pervs but responding to your statement, "If you're already a native English speaker you do not need tutoring in English." -- I don't agree fully with it. A native speaker can speak well with their family and friends, can chat with others, but...they may not speak in a conference or any meeting or may not write a formal letter or any such things that need a formal setting without any error(grammar, punctuation etc.). They may also need help for proofread or edit their thesis or any such academic paper.
So, just because they are NATIVE English speakers, that doesn't mean they are good at it. They also need helps, who knows...:)
I agree with all the above comments. Most if not all of these messages come from scammers, or simply simpletons. On the other hand, for the sake of clarity and keeping our minds open, I want to add that not all Americans are native English speakers. There are a lot of immigrants to the United States (as well as of course to other English-speaking nations), so that many Americans are second language speakers of English. What's more, as Troglodyte pointed out, there are plenty of native English speakers who could use help with their writing.
That said, I doubt very much that the people who are sending Alice these greetings and declarations of interest are serious learners, of English or anything else. I'm a senior citizen with a much less active presence here, and even I receive a couple of these messages every day. I make it a practice of ignoring anyone claiming to be American who sends me a message, unless they articulate some particular reason they are writing, such as a response to a discussion comment or to a notebook entry. @Alice, maybe you want to consider just ignoring the obvious time-killers.