Chametz owned by a Jew during Pesach is forbidden after Pesach, even if the person owned the chametz "accidentally" - e.g., he forgot he had it or he didn't realize the severity of the prohibition of owning chametz on Pesach.
So you're correct: If the owner of the supermarket is Jewish, then it is forbidden to buy chametz there after Pesach. Rather, you have to wait until enough time has elapsed for him to be able to sell his entire stock of chametz and purchase new chametz.
Certain supermarkets of Jewish ownership in fact follow the custom to sell their chametz to Gentiles for the week of Pesach. Some Halachic authorities question the validity of this sale, however, since a non-observant store-owner probably views the sale as a mere formality and not as a binding contract. Especially if, after selling his chametz to the Gentile, he turns around and sells the chametz to his customers during Pesach.
Rabbi Moshe Feinstein rules that the sale is clearly valid. When the owner goes ahead and sells some of the chametz to his customers, he is simply re-acquiring that chametz (although he may very well be considered stealing). The leftover chametz, however, remains the property of the Gentile and can therefore be eaten after Pesach. This is because the owner wants the sale to the Gentile to take effect wherever it can, in order to "save" himself from the transgression of owning chametz. Even though we see that he is prepared to go against the laws of Pesach, he does so out of a motivation for personal profit and not because he wants to violate Halacha. Wherever he is able to keep the Halacha without losing out, he wants to keep the Halacha. So, concerning the remaining chametz, he wants the sale to the Gentile to be valid..
However, Rabbi Feinstein points out that it is nevertheless forbidden to buy chametz from such a store after Pesach. Why? Because the sale applies only to chametz owned by the store at the time of the sale. Any chametz the store purchases later - i.e., during the week of Pesach - is not included in the sale, and therefore forbidden during and after Pesach. Unless the store receives Rabbinical certification that the chametz was sold before Pesach and that no "new" chametz was brought in during Pesach, it would be forbidden to buy chametz there after Pesach.
In Israel, the circumstances are somewhat different, since the stores generally do not replenish their shelves with fresh chametz during the Holiday. Therefore the only relevant consideration is the validity of the pre-Pesach sale of the chametz to a Gentile. Rabbi Yosef Shalom Eliashiv, shlita, insists that special clauses be added to the standard contract for the sale of chametz in order to emphasize the seriousness of the sale and ensure that the sale is "for real."
The custom of the Vilna Gaon was not to buy any chametz that was sold for Pesach. This was based on a concern that the sale of the chametz was not 100% valid. Although some people today follow this custom, it is a chumra (Halachic strictness) and not the standard practice. Furthermore, some people only buy chametz made from wheat which was ground into flour after Pesach. This is due to a concern that the flour ground before Pesach may have come into contact with water.
- Shulchan Aruch, Orach Chaim 438:3.
- Halichot Sadeh -- HaGaon Rabbi Yoseph Shalom Eliashev.
- Iggrot Moshe, Orach Chaim 1:149, 2: 91.
- Siddur HaGra.