Maybe I'm not sure about how tech-savvy most people are, but when I get a text message from an unknown number claiming to be my provider asking me to click a web link to update my phone, I know something's up.
It doesn't have to be an unknown number. Certainly in the UK, it's pretty easy to send an SMS with any name (text or number) you want in place of the phone number. And I suspect that most people aren't that tech-smart to realise that a text claiming to be from T-Mobile isn't actually from them.