This actually makes zero sense if you think about it. If the client is receiving messages via SMS, then strip the HTML. If it's a browser or API client, show a richer version.
No reason the lowest common denominator must dominate.
In most messages, the links are as important as the message itself. If you're going to selectively remove links based on how the client sees the message, then you're essentially changing the message itself based on how the client receives it. Which is wrong.
I guess what joshu was trying to say, is if you're receiving SMS, then a url with that is useless. You can't look it up on your phone, and if you can, then use twitter on your web browser instead of SMS. Even including the URL would mean you'll have to wait til you get a computer, at which point you could just visit twitter anyway.
No reason the lowest common denominator must dominate.