If the label contracts were structured as loans that had to be repaid, I agree with "completely false".

But if, as I suspect, most contracts were structured as advances, then if the musician was successful, you could look at it as the musician just having gotten a loan.

But, famously, most musicians aren't very successful, and they aren't in general asked to pay back their studio time.

So I don't think "completely false" is a reasonable response to "the label paid for studio time".