There's a few things wrong with this statement. Calling it a European invasion is the first. There isn't a monolithic European culture as demonstrated by the current EU difficulties. The invaders represented distinct cultures and didn't see themselves as one and the same or even 'European'.
Furthermore, there is a Western bias in considering all 'Indians' as one population. They didn't see themselves that way at all. Instead, they behaved and warred as distinct peoples and cultures and didn't even share languages. The Americas are and were quite diverse with the affected populations geographically limited. Try calling a Mexican a Guatemalan and see the response. The modern liberal term Hispanic is another such contrivance.
Finally, the population numbers of extant pre-Columbian peoples in the Americas varies wildly depending on which 'expert' you consult. These people were dying from disease, famine and war long before Cristobal's 'discovery'. The danger in focusing only on the post-Columbian experience is that it serves to further the Left's agenda. I do understand your perspective and point, but it deserves a clearer picture and more explanation.