Problem with PWM interference
Well, your PWM outputs are both on 16b Timer/Counter 1 and the servo is attached to the 8b Timer/Counter 0. So my guess is that 8bit counter has too low resolution for driving the servo and it uses Timer/Counter 1 in full 16b mode for better precision instead (PWM uses just 8bits from 16). Also Timer/Counter 0 is used for counting millis, so its settings can't be changed anyway.

For the confirmation you can either:


use pins 5 and 6 (TC0) or/and pins 3 and 11 (TC2) and for the servo use pin 9 or 10
You can read the values of TC1 configuration registers and according to the datasheet you can figure out what mode is currently used.


EDIT:
So on the Uno board is used Timer/Counter 1 for timing purposes:

  if(timer == _timer1) {
    TCCR1A = 0;             // normal counting mode
    TCCR1B = _BV(CS11);     // set prescaler of 8
    TCNT1 = 0;              // clear the timer count
    TIFR |= _BV(OCF1A);      // clear any pending interrupts;
    TIMSK |=  _BV(OCIE1A) ;  // enable the output compare interrupt
    timerAttach(TIMER1OUTCOMPAREA_INT, Timer1Service);
  }


So no PWM on the OC1A nor OC1B in normal mode and the channel A is taken by Servo.