You probably could look at homes up to $75,000 or even a little more assuming that you could negotiate them down to $70,000 however I would tend to agree with your Realtor. $70,000 is the maximum you can afford per the lender, and just because you can doesn't mean you should. Trust me and your Realtor, if you can find a home you can buy for $60,000 you'll be much happier. You'll be able to make your payments easily and won't be pushing the envelope. This is as true for you as for someone who could get a mortgage for $700,000. There's nothing wrong with living slightly below your means. I applaude your Realtor for not pushing you to the max, it sounds to me as if you're in good hands.
I wish you the best of luck and happy house hunting.