At least in the UK (and yes, I have checked this with a lawyer) when I altered the contract before accepting a job, their paying me is deemed to be acceptance of my changes. I am surprised that the same doesn't apply in other common-law jurisdictions.
I admittedly haven't specifically checked this with a lawyer. My comment was based on a discussion with a former boss, but I cannot verify that it is correct.
However when I think through the principles of what makes a contract under common-law, it does make sense that payment would constitute agreement to the contract.