you heard wrong. What most electricity grids forbid is exporting power from your home to the grid when the grid is down. The claimed danger is that energised power lines will kill people working on the lines.

The reality is that the vast majority of home inverters (in an EV, battery or solar PV) is nowhere near powerful enough to energise even a single distribution transformer.

This is yet another example of electricity codes being unrealistically restrictive.

Generally, there's nothing stopping you from disconnecting your home from the grid during a power outage and running your own devices off a battery. Going fully off-grid depends on your local laws.