Yes, it has higher voltage than the grid voltage. Unlike some people describe the grid is not low impedance. Just with electronics terms. You have a feeder, this is usually a HV to LV transformer, on it's output you have 230V. You connect 10 houses to it. They are in parallel, but they have different length cable connecting to the grid. So house 1 will see 229V, house 2 228, house 3 227, house 10 is 220V. You are house 4 you have 226V before you turn on the inverter. After you turn it on, it is 228V. So current will flow to house 3 also, and the voltage for house 5,6,7 will increase (current flows that way also).
If all the homes have solar panel, and they dont have load at the moment, the voltage can increase above the grid's limit, and some of the inverters will turn off. And the voltage will be the lowest at the transformer.
Also, notice how it takes power to raise the grid's voltage. Power, which comes from the solar panels. So it cannot really go haywire and mess up the network, by inserting 1000V into it. It can mess up the harmonics though.