Sounds like just another buggy KVM switch to me.

The basic problem is that the I²C used to read the EDID assumes that you only
have two endpoints on the wire - the display and the gfx hardware. So properly
designed KVM switches have an micro-controller which fetches the EDID from the
monitor on connect and forwards the EDID to each connected system if requested.
Otherwise you run into problems when by pure coincident two systems try to
fetch the EDID at the same time.

Without the EDID the gfx hardware has no idea what resolutions the display can
handle and most likely doesn't choose the optimal one. Easiest workaround is
manually set the necessary resolution for the display.