Not completely true. There was population movement from central and eastern Balkans but it's impact is hard to measure due to lack of proper sources.
Theory I wrote is coming from book about Serbs in Croatia written by local Serb. Vlach question is very complex.
There are different Vlach groups:
1. Istro-Romanians/Čići - by origins from Transylvania or Banat, speak arhaic Romanian and very small in numbers
2. Vlachs in eastern Serbia, also Romanians by origins and Istro-Romanians are possibly connected to them
3. ''Morlachs'' (which is a exonym) or Slavophone large population of dinaric alps, who are most controversial here and their origins are most disputed
4. Aromanians or Vlachs proper who are only present in south of Serbia, but their connection with Morlachs is proposed, but only partially.
Hypotesis goes like this: Morlachs are either native Slavs mixed Latinised Illyrians of western Balkans, or they are Aromanians from east and central Balkans who admixed with Slavs and lost their language trough centuries.
It's interesting how close you are to Morlach cluster average.