"... long-term camp consisting of six consecutive days and five nights of resident camping, approved and under the auspices and standards of the Boy Scouts of America."
It does not say that the resident camp must be at a Boy Scout owned or operated facility. If the national Order of the Arrow committee had wanted to say that, they would have. The language used was very carefully composed. If a troop runs their own long-term resident camp, "under the auspices and standards" of the BSA, it qualifies. The BSA does have very explicit standards for a resident Boy Scout camp, requiring much more than just a week long campout. Your local council camping people can provide more information on what the current standards are.
Some of the confusion may be caused by an error in the current Boy Scout Handbook, which stated the camping had to be at "a local or national council facility", but that is incorrect.