I had a small epidemic of flat tires last month on my old bike. I think the second flat was caused by a tiny piece of glass still embedded in the tire. I went over that tire several times and could NOT find it, but my eagle-eyed husband finally spotted and extracted it.

THEN.. I bought a nice new inner tube, which not only went flat almost immediately, but when I blew it up to patch it started springing new pinholes all over the place!! I've never seen anything like it. I threw it away and get another new tube, which has been fine.

So, even if no one else does, I believe you that you got a defective tube!