All of that may be true, but unless the timeshare has your social security number, they cannot report your failure to pay your maintenance fees to any of the US credit bureaus. In addition, they must be a member of a US credit bureau to report to it. This is based not on opinion, but on my 30+ years of experience as a banker who dealt with credit on a daily basis.
I know that we didn't give our social security number to anyone when we purchased our timeshare weeks. But even if we had, again the timeshare must belong to the US credit bureau in order to report through them, which is highly unlikely.
For that reason, I would think that the original poster is safe to give up their timeshare without concern that their credit rating will suffer.