I think you both misunderstand. Matter can and does bend space, but without matter to bend it, and in particular on larger scales, space is flat insofar as we can tell. There have been pieces in The Sky at Night magazine recently.
(FWIW, I did physics and astrophysics to degree level, though freely confess I didn't finish - but I have kept up to date. Last year I bumped into someone from my school who went to the same university and did the same degree. He teaches physics and has worked at several large telescopes (even has an asteroid named after him) - my ego was plumped up by being able to comfortably converse at the same level, and by the fact that my understanding of orbital mechanics and why the Lagrangian points are stable was better than his. So it wasn't all wasted.)