Is it true that if I work overseas as a contractor I can pay zero taxes?

Yes and no. If you are self-employed and you live overseas, you may still be required to pay self-employment taxes in the US, including Social Security. This would need to be paid before the Foreign Earned Income Exclusion (which can exclude up to $105,900 of your 2019 income from US taxation), so it is an actual out-of-pocket expense, not something that would be offset on your expat tax return. The rules are different for each country, so visiting the Social Security website is the best way to see how this will work in your exact host country.