As someone who has been there, it sounds like something I would walk away from.
I've been doing freelance contract work for a little bit now, and early on, I took on a project where very little was in writing. Since the contract was basically "the developer will get paid x amount of dollars for his 'web development' services", I was eventually extorted to do more work than we initially talked about in our verbal agreement. Because the contract didn't outline what 'web development' meant, I had no leverage in persuading the client that my work was done. I agree with one of the previous posters that the job title itself doesn't matter a whole lot, but at the same time, if you are asking for something reasonable to be in the contract, but the employer refuses: huge warning signal.
Since then, I've turned down a couple deals that were really enticing financially but had a couple similar red flags to the ones you've pointed out. It was rough to do so at first, but I sure haven't regretted it since, and I think I've saved myself a lot of heartache.
tldr; get everything in writing!