Why would they out-compete the third world?
Much, much higher productivity and much, much better infrastructure.
As for the second point, I guess any country is allowed to do whatever. But since the tariff hurts the country itself it's a bit silly and I think overall free trade would be a better solution.
Sadly, many third world countries are not allowed to do whatever they want, because they receive money from the WTO/IWF.
And the western countries, who rule these organizations, force them to open their markets, while they themself keep subsiding their agriculture and industry. Shameful even from a free market capitalist point of view.