Analog recordings are still bandlimited, moreso than your standard digital file. Way more than a 192kHz digital file. They have quite a bit of treble rolloff.
The distortion would arise when a headphone is trying to reproduce a frequency that it is not really engineered to reproduce, which a 192kHz file is capable of producing. Really a worse case scenario though I think.
What does sample rate have to do with frequency limitations? Wouldn't that be caused by bitrate?