No offense, that's not my understanding of what happened. And that's not what was shown in the histories. Do you have any documentation to back up your statement?
Again, that's not what my experience showed. I'd always been taught that the true Bosnians were the muzzies...and that there was a distinct difference between the (largely Catholic) Croats and the (largely Orthodox) Serbs and the (largely muzzie) Bosnians. There may be no genetic difference, but, from what I saw over there, there was a cultural one.
That was due to Ottoman occupation, what you were taught versus the reality of the matter are different.
The Serbs were a greater part of Bosnia's population until only the last few decades.
Back during Austrian rule the census had Serbs in the low 40% range and Muslims in the low 30%, so a reverse of what you have today. Then consider that there are "Bosniaks" in the Sandzak (region that covers part of Serbia and part of Montenegro) who never lived in Bosnia nor did their ancestors. They were given an identity by the Ottoman Turks.
Izetbegovic himself had parents who came from Belgrade, and a great many other Bosnian Muslims had ancestors who were originally from Serbia or Montenegro.
Additionally, many Hungarians and Albanians who settled in Bosnia over the last 150 years are now "good Bosniaks" - and this according to a Serb and Croat hating Bosniak himself. (There were also many Ukrainians who were brought over during Austrian rule, and most of those became Croats or mixed more with the Croat Catholics.)