Having done a relocation with my wife's company, you see how the HR department really works. And if you think it's important with day to day, it's doubly so with a relocation.
And based on what has happened with respect to your offer, I would seriously question the integrity of the HR departement.
Keep in mind, you will have to deal with HR at some point. Be it for promotions, pay raises, or even unhappiness with you desk location. Additionally, should you have more serious issues like not enjoying your assignment or your boss turns out to be a jerk, you will be completely dependent upon their HR department for handling these issues.
It sounds like you will be dealing with a less than diligent (and possibly unscrupulous) HR. To some extent, HR is a reflection of the upper level management. So you should not expect much different from upper level management.
Don't walk... RUN!!!