Not sure if it flags as fake but I'd look into getting a dedicated Twilio number, then just forward incoming texts to your email or something like that. It would at least get the "shady" part out of the equation as Twilio is pretty trustworthy.
> as Twilio is pretty trustworthy.
as considered by who? do banks accept a Twilio number as a valid number according to their security best practices?
This does not work, I've tried this before. Google verification for example would not accept my Twilio number as verification (about 2 years ago). You can lookup a phone number for the provider and numbers from Twilio or others tend to not be accepted.