Simple counterproof: any country with very different GDP per capita but equal economic complexity index.
Economic complexity directly measures the "more capital, more reputation, more knowhow, more relationship with existing customers" that you claim is important.
If the relative rank of economic complexity deviates from the relative rank of nominal GDP per capita, then it means nominal GDP per capita is not captured by measurable technological capabilities but by other factors.
According to this Economic Complexity ranking, Slovenia, Slovakia and Chechia have a much more complex economy than both US and China. South Korea is number 3 in that list compared to US which is number 14. I have a hard time believing this complexity ranking. I do like this website for the huge economic data they provide in terms exports and imports of various countries. But I don't think their methodology for calculating economic complexity is good.
Edit:
Okay there are even more gems in this ranking, Mexico has a higher complexity than netherlands and Denmark. The same netherlands that makes ASML lithography. Yap, very accurate list.