hcubature does not converge on discontinuous functions

As discussed in https://github.com/giordano/Cuba.jl/issues/16, hcubature seems to fail for a discontinuous integrand (see MWE there). The integrand is the indicator function of a polygon, so a Riemann sum with NxN points should be accurate to 1/N, and the integral should be about 0.88408, with a small error on the last digit. When running Cuba vs Cubature for decreasing values of abstol (reltol and maxiters are fixed at 0), I get:

0.8840847072116771 ± 9.995513758054815e-5 (Cuba.jl)
0.8848895327256797 ± 9.998142861595564e-5 (Cubature.jl)

0.8840898028407925 ± 9.998969682594401e-6 (Cuba.jl)
0.8848941514595511 ± 9.999535960807015e-6 (Cubature.jl)

0.8840867311005485 ± 9.99974855348049e-7 (Cuba.jl)
0.8848940796576487 ± 9.999981972972212e-7 (Cubature.jl)

0.8840865507480177 ± 9.999859751764881e-8 (Cuba.jl)
0.8848940808860499 ± 9.999994401879008e-8 (Cubature.jl)

So Cuba looks about right, but Cubature appears to fail in that case.