I would imagine magnetizing a mechanical watch would really mess things up, so at a "just under really messed up" threshold it would probably have the claimed effect.
You may be thinking of YIG garnet oscillators which are very dependent on magnetic field but they haven't been common tech in maybe 30 years. Even used on ebay they cost more than modern new microwave VCOs which is annoying. I have a box of old YIG osc in my basement which I actually used for ham radio experiments before modern solid state VCOs took over.