You're not being silly.
Most camera lenses use varifocal lenses so you will lose focus when the focal length changes i.e. when you zoom in and out. The camera's processor is probably not quick enough to autofocus quickly enough to make the loss of focus imperceptible.
I'm not hugely familiar with the FZ48 but if it has a manual mode for video recording, can you make your aperture smaller to get a deeper depth of field while bringing down your shutter speed? You may still lose focus when zooming in and out but it might not be as big a loss so the correction may be quicker.
DSLRs: Canon EOS 7D Mark II, Canon EOS 70D
CSC: Canon EOS M3
Lenses: Canon EF-S 15-85mm f/3.5-5.6 IS USM, EF 50mm f/1.8 II, EF 100-400mm f/4.5-5.6L IS USM, Canon EF-M 18-55mm f/3.5-5.6 IS STM, Canon EF-M 22mm f/2.0 STM