If there is a quote, it is not a quote about “benefiting from electricity on Shabbos”.
The reference to the Hazon Ish is referring to benefiting from the electricity produced by Israeli Power Plants that have Jewish non Shabbat-observant employees working on Shabbos.
The Hazon Ish writes (Orah Haim 38:4),
If the electricity was produced by a Jew who is not Shabbat-observant, it is forbidden to benefit from it. Even if it is a situation in which Halachah technically permits benefiting from the electricity produced, it is [still] forbidden since its use constitutes a chilul Hashem (desecration of God’s name)… because it is a public service, and the worker who [maintains the power plant] on Shabbat does so in a rebellious manner. One who benefits from the electricity produced in this manner indicates that his heart is not pained by the desecration of Shabbat [by other Jews]. May it be God’s will that everyone should speedily commit to a complete teshuvah (repentance)!
The moshol (whoever said it) is referring to the callous lack of pain at Chilul Shabbos and Chilul hashem shown by using electricity produced with the assistance of a Jewish person on Shabbos.