More pointedly, Key and Santos had also just emerged from talks in which trade dominated, including an agreement to assess the potential for an economic partnership between the two countries - a possible precursor to a free-trade agreement.
The hats are a national symbol - but last year they also became a symbol of the problems of trade. The Economist wrote that cheap Chinese imitations of the handwoven hats were flooding Colombia for little over a tenth of the price - a situation that eventually prompted authorities to ban imports of the knock-offs.
The episode illustrated the sensitivities over trade - and as New Zealand and Colombia both have substantial agriculture industries, they could arise again.
Nonetheless, taking questions afterwards, Santos surprised and delighted the New Zealand delegation by saying he was interested in a free-trade agreement with New Zealand, if it was ready for it. Asked if it was safe for businesses to invest, he said the rate of foreign investment into Colombia was rising more quickly than in any other country in the region, indicating companies believed it was a safe place to do business.