Arduino Due - Serial speed?

very simple code:

int x;
void setup()
 {

Serial.begin(250000);

randomSeed(analogRead(0));
  }
void loop()                  
{
     x=random(300);
     Serial.println(x);     
 }

IDE 1.5
The board is connected through the programming port.
Putty shows correct list of numbers coming from virtual COM.

If you increase speed to, say, 252000 or even 251000, Putty shows garbadge.
I played for couple hours trying to find any combination of Arduino/terminal program speed settings >250000 which does not produce garbage, and I failed.
With Arduino MEGA same code generates correct transmission up to 2048000 May be even with bigger numbers, but I feel it does not make sense to go further, because it is not the actual transmission speed. It is just some correct handling of parameters, like, if speed>2500000 then speed=250000.