Why do I find this hard to believe?
Because you haven't done the math?
Assume a 300W panel. Size is around 2mx1m. That single panel should generate roughly 1KW in summer or 400W in winter (rather low ball numbers, actual will be higher). In say an average small house, you'll have about 10 x 6 roof space usable - so say 60sqm up top.
30 panels would be more than sufficient (giving you 30KW+ in summer minimum, and say 12KW+ in winter), and still leave room to spare.
This doesn't take into account evenings and storage, but reducing daytime use drastically allows Eskom to power down a couple of coal stations, or run more at lower capacity, increasing existing life spans. If Eskom / muni's put some motivation into play for consumers to do this - i.e buy not actively penalizing you like they do now, you'd probably see more uptake. This would also make more excess available for the non paying consumers, as its likely it would be generated by solar.
If Eskom and Muni's don't come to the table, people will just go offgrid (eventually), as their pricing will make it too attractive not to.
That will just leave the non-payers on the table for Eskom, and really really expensive Nuclear being unaffordable for the country.