I will have worked at my job for 3 weeks shy of one year when I am due to have my son. I asked off beginning August 1, I am due the 8th, and my company told me that they could not accept this. I was under the impression that The Family Medical Leave Act says 1 year and 1250 hours, but recently someone told be it was either/or not necessarily both. They haven't been the most accepting of my current situation and I am wondering if they are bending laws or if they are completely within their right.

No, it is not either/or - it is 12 weeks AND 1,250 hours. That's right in the statute; it's not open to interpretation.

It's not either/or. It's both. You have to worked for the company at least one full year and you have to have worked 1,250 in the past year. Thus, you are not eligible for FMLA leave on August 1st.