While it is usually the case that lower unemployment leads to higher inflation, it is not set in stone. Yes, countries without full employment are 10% more likely to have acceptable rates of inflation. But there still remain 24 countries that have had full employment in the last 5 years that have also had acceptable rates of inflation. In other words, there are 24 exceptions to the rule! That's a full 28% of countries that have had acceptable rates of inflation in the last 5 years! And what about the countries with unacceptable levels of inflation? What are their unemployment rates? 66% of them do not have full employment. In other words, a country with unacceptable inflation is twice as likely to not have full employment.
Here is a list of countries/provinces that have had full employment and acceptable rates of inflation in the last five years:, Macau, San Marino, Vanuatu, Hong Kong, Northern Mariana Islands, Japan, Norfolk Island, Singapore, Brunei, Liechtenstein, Switzerland, Gibraltar, Norway, The Netherlands, Denmark, China, Monaco, British Virgin Islands, Taiwan, Austria, Ireland, Luxembourg, Cyprus, Lithuania, Palau, Australia, Bermuda, South Korea, Bhutan, Malaysia, New Zealand, United States, and Iceland.
Another large hole in the theory is that countries with full employment actually have lower inflation on average.
Average inflation rate of countries with unemployment below 5% (considered full employment): 4.52%
Average inflation rate of countries with unemployment above 5%: 5.34%