I wouldn't "leg it" if I were you - you never know you (or your new employer) might deal with them in future.

Ben made some great advice re documentation - if there is no documentation or paper evidence then it would be questionable. Even if there is a documentation supporting the evidence, as long as this admin thing you have to do is achievable/not impossible, then I would stick to it for a 1-3 months.

If you think about it, you are only with them for 6-7 hours a day and there are 24 hours. :o)

Just my 2pence.