Hypothetically, if I have something web accessible, and you are accessing it, it becomes unauthorized as soon as I (the owner of the service) tell you that you are no longer authorized to use my service.
Analogies rarely work -but it's sort of like how it's trespassing once I tell you to never come on my property again.
I also have a publicly accessible email address and phone number for my work. Should it be OK for someone to keep calling me incessantly and lock my phone line such that no one else can come through?
Of course not, and that's why there are tools to protect against phone and email spam, and that's why it's good to be polite and not abuse a service. Especially a free service.
Twitpic have a publicly accessible http server. Sending it http requests is therefore something they've implicitly allowed.