Well, yeah, I would. I would never dream of calling them from my cell phone. I learned from giving out my landline all the time that this is a recipe for junk calls. My cell number is given out only to people I know and trust, period. My landline is like my junk email.
I’m also just more careful with information in general. Everything I’ve read suggests we’re all too sloppy with sharing information online. Humans just underestimate the specificity of data, or don’t realize ho a single big of key information can give out tons more data about you. I’m not going to make that worse by giving out key information.
Even if I trust Twitter, Twitter can be hacked. And Twitter uses advertising, which is always shady in sharing info among several groups.
The risk may be small, but I see no reason to make it worse. I’d be more likely to just give up my account and move on than to use phone number verification. I’m no one special, and no one follows me.
Then again, there’s no way Twitter would ever get my credit card info, either. At that point, the OP might as well just give them his number. They either already have it or could easily get it.