If B2 and D4 are positive, then in the marginals B,D,2,4 will show positive, but you don't know which of B2, B4, D2, D4 are positive.

Yes that is true, but when the case rate is low this is not a common problem. The ideal size of the grid is adjusted to expected case rate.

If you get ambiguity then you just move those samples across to a new grid (in locations that won’t be ambiguous) and test again.