In episode 11 - Hollow Touch, we learn that the prevailing myth among humans about how half-spirits are born, that if a pregnant woman is spirited away, when she returns, the baby later born is a half-spirit, is incorrect. The real reason was that the Village of Oracles would take pregnant women and put them through a ceremony where the blood from a severed fox spirit's head is poured on the woman's stomach.
We know that the chief of the Village of Oracles has had numerous half-spirits born before, as when Zakuro was born he had plan to put her with the rest of the half-spirits, that was until he realized what power she had. Even after Tsukuhane's escape, the village chief, and later Lord Omodaka, continued in an attempt to create another half-spirit with Zakuro's power.
Susukihotaru, Bonbori and Hozuki are all half-sprites. Kushimatsu did say that she traveled with Zakuro, finding half-spirits and taking them in to protect them from the Village of Oracles. But if the myth about a half-spirit's birth was actually the work of the Village of Oracles, then how were those 3 born as half-spirits? Bonbori and Hozuki was raised in a cave, and if the 3 were born in the Village of Oracles, Kushimatsu would not have been able to rescue them.