the LPC9xx's have an extension (as compared to the "biblic" '51), so they are able to toggle a pin upon timer overflow - that's hardware, so no interrupts nor other sw needed.
Sure, but that does not achieve 3.xx MHz. Split timer with auto reload and Tnout will give? is it 1/8 or 1/4 oscillator freqency. With PCLK at 3.xxx MHz and the toggle in the output, the max will be 1.xx MHz I do not recall if auto-reload of ff gives "clock in = clock out" or "clock out = 1/2" clock in" thus the frequency on the pin will be either 7.xx/4 or 7.xx/8

The real issue with the question is that the poster totally ignore the interrupt 'overhead'.

Erik