It is true that developed and prosperous nation would have ripple effect on the nations around then or associated with them. Thus I am inclined to partially accept the speakers views that nation will thrive if all other countries around it are in good state. There is only one option that negates the speakers view that is an hostile nation is also being well and progressing.
Firstly if we consider that a two nations have common interests and they are willing to cooperate with each other in terms of economy, defence hence forth. Then we would see that dynamics of both nation effecting each other for good. Many pacts and agreements would be signed between them which would benefits both. For real world example we see that China and America are both striving together for their nations, they are the greatest trade partners. In fact their economies depends on each other, if there are crisis in any one, other would be impacted definitely.
Secondly if two countries are neighbours then the ripple effect would be even more stronger and correlated to both. For instance if one of the country is going through famine then this would have an visible negative impact on other country, there would be likelihood of refugee scenario or the drought would cause many inadverted cancellation or distortion of business pacts. Similarly regular imports would be effected even more. Economics condition of neighbouring countries is very much tightly dependent on other in one way or other.
Ultimately this could be concluded that if all countries in the world are thriving this would have an positive impact on the over all world. As they share the same planet they are naturally associated with other. Thus if most nations are thriving and flourishing there is a tendency that these nation would like to solve outward problems if their domestic issues are calm. World would be a better place for all if most of the people are living in harmony as it is naturally human are inclined to help them who are in need.