Neither. "The earth is not a closed system" is correct and does NOT contradict the comment "our solar system can be treated as a closed system". Why---because the SUN is a major source feeding external energy into/onto the earth's "systems". However, the "solar system" has no such large external energy source.
My point -- see the bolding in the part of the article I quoted -- was that the author was being dishonest or dumb in conflating the two.