OLED on Hardware SPI, on DUE
It doesn't look like it's true. There is only one SPI module and it has fixed pins which are not duplicated anywhere.

However there are three instances of USART which can be used in synchronous mode as SPI:


USART0: RXD0(PA10) / TXD0(PA11) / SCK0(PA17) 
USART1: RXD1(PA12) / TXD1(PA13) / SCK1(PA16)
USART2: RXD2(PB21) / TXD2(PB20) / SCK2(PB24)


Whole table from SAM3X datasheet:



But I'm not sure if the Arduino IDE supports this mode, or you'll have to do it from scratch by yourself.

You can even use RTS as select slave signal: