Can't because named driver or will lose insurance

Need to be specific about terminology here.

Was she looking to be a named driver on her mother's policy or was she looking for an insurance policy on her mother's car in her own name?

Most likely they asked the insurer exactly what OP stated and the insurer said they’d wouldn’t be able to use their no claims bonus or would lose it on their own insurance. Presumably they actually want to be named though, which shouldn’t be an issue and something insurance companies deal with all the time. So as above, sounds like a communication issue, but very unlikely they were told they’d actually lose insurance on their car.