This is right. A proper system has a transfer switch that prevents back feeding the grid if it’s down. There’s also a safety aspect in that supplying power to the branch circuit in this way bypasses the overcurrent protection, so one could potentially be loading that circuit with 5 A on top of its rated load and cause significant damage.

If a person wants to offset their electricity at this small scale, better to have it powering a shed or charging power tool batteries. Won’t get as good a return, but you’d never get a return on a permitted grid tied system at that scale either.