Well yes and no. Overcurrent failures are not caused by receiving too much power, but rather by drawing more power than the wiring is capable of handling.
There's always orders of magnitude more power available on the grid than could safely be pulled through your house's wiring. However, your wires don't burn up because the actual current draw through those wires is always much less than they can handle, just like that filament I described, through which the current draw is near zero because the air has very high resistance and thus sinks very little current. Each house has breakers or fuses to ensure that you never draw more than the wires can handle (or at least not for a long enough period of time to damage the wires).
In a similar way, if solar panels on the roof are producing more power on the roof than is needed by all of the consumers, that typically shouldn't be a problem. It only becomes a problem when someone consumes that power through a circuit path that wasn't designed to handle it or when it causes mechanical generators to go berserk in some way.
And power flowing through an insufficient circuit path means that either the solar panels are allowed to produce more current than the house wiring was rated for (which should result in fines for the installer that put in the oversized master breaker without getting the line upgraded) or the feeder line into the neighborhood is actually too small to handle the all of the houses using their maximum current rating at the same time (in which case the system was designed dangerously to begin with, and the power company just got lucky before). Either way, the problem isn't specific to solar power generation being present.