No, the high voltage was at very low current, just used to put an electrostatic charge on the selenium drum. Fires came from the fuser, where the toner is fused to the paper with heat. Paper jams could cause scorched paper and potentially a fire. Thermal fuses, switching from radiant heat to a hot roller, and lower melting point toner fixed that in laser printers.[1]

[1] https://www.wired.com/2015/03/whats-inside-printer-toner/