If they're just specifying a font (e.g. 'Helvetica') in their CSS, it's loaded from the users' machine and doesn't cost anything.
Otherwise every site on the internet would be paying fees for fonts.
I could be wrong. Please inform me if I am.
IANAL but this is only true in some jurisdictions, primarily the US and Japan.
Also, I don’t think it’s quite that simple either. The actual type face may not be eligible for copyright, but the computer code describing the particular curves and hinting rules and etc. is. So I think you can’t just trivially copy a font and modify it and call it your own.
Warning: offer not applicable in UK and most countries in EEA. They have the concept of protecting designs there. Japan excludes most designs of fonts because of its utilitarian use BUT if the font (technically typeface) is distinctive and used in a way that can be defended as an artistic choice, it's protected under copyright.
It's always more economical for a company of Twitter's size to develop their own font because 1) Then they don't have to pay per-use licensing fees, which are huge at the billion user scale, and 2) a peculiarity of copyright law means that the actual shapes of the letters aren't actually protectable by copyright -- you can copy an existing font virtually 100%, tweak a thing or two, and legally call it your own.