Technically it is correct. The rules are that any cables grouped together have to have insulation ratings for the highest voltage cable that they are grouped with. The reason is that if the insulation were to fail on the power cable then contacted the outer insulation of a cable like HDMI, the insulation would leak voltage into the cable and pose a shock hazard.
You can ask that it be run through a separate hole and that would be perfectly acceptable to the rules, just a few inches apart is fine.
Looking at one of my HDMI cables the insulation is rated for only 30V, much lower than the 600V of a power cable. You can check your cables or other wires by just reading what is printed on them , it will list the voltage .