Maybe the article neglects to repeat that the parameter

thas to be positive; but it has little practical importance beyond culling sectors 1, 2 and 3 (because they don't contain the ray's starting pointpand the direction vector points between up and right from somewhere in sector 4)

Sector 4, on the other hand, is guaranteed to contain an intersection because it containsp.

Yes, I know that, but I need to use the algorithm for octree ray traversal and I don't see the solution with this algorithm when t is negative. Does the solution exists?