Boeing Wire Harness Design Engineer interview questions

I was contacted by a recruiter through a staffing company in April, 2017. She submitted me and I was called for an interview. The interview was with 2 people, over the phone, lasting about 30-35 minutes. The majority of the questions were simply asking about my experience or familiarity with certain programs, and the generic "why here/now/etc" and a few behavioral ones. The recruiter contacted me about 10 days later to tell me they had made me an offer, and gave me a formal, written offer with the contract length, hourly rate, etc. The next day, however, I was called by the recruiter who informed me that Boeing apparently gave me the wrong amount...and lowered it quite a bit. I informed the recruiter that I found that to be very disrespectful, and to tell Boeing that I wouldn't be considering anything below what was already on my written offer. Boeing said they were not going higher than the new number, which was quite a bit less (despite the fact that the number I have on the written offer sheet is very much a normal amount in line with the level and location of this job).