Beets on Pesach

Many have the custom to eat borscht - beet soup, or just beets, on Pesach. The Belzer Rebbe, R. Yissachar Dov Rokeach, once related:
"I always wondered what the reason for this custom was. I asked many great people, but no one knew why. I once happened to be with some great sages from Lithuania and they told me the following reason:
The Tzadokim, who denied the Oral Torah, interpreted the passuk "כָּל-מַחְמֶצֶת, לֹא תֹאכֵלוּ - You must not eat anything leavened" to also mean anything which has a sour taste (the word "חמץ - leaven" sharing a root with the word "חומץ - vinegar"). Therefore, the Tzedokim would not eat beets on Pesach. To show that they did not support the Tzeadokim’s ruling, devout Jews adopted the custom of eating beets on Pesach."
בשם האדמו"ר מהרי"ד מבאלזא, הובא בהגדה של פסח מדרש בחידוש עם הוספות אמרי קודש על הפיסקא "מצה זו." בשם החידושי הרי”מ, הובא בספר “חשוקי חמד” (זילברשטיין) ברכות לט, א. “הלכות והליכות” (רלב”ג) ע’ 40