External pull-ups give you more control over how fast the capacitor charges. The internal ones are 50k to 80k which is close enough to the value used here that it'd probably work ok.
Mark also pointed out that throwing some "extra" resistors in gives you more points at which you can tweak the circuit and fix design issues that slipped by. You can always remove a resistor, change its value, swap it for a 0-ohm, or even solder a wire to another voltage source or ground in case you made a mistake in the schema. So having these resistors might not hurt, even if they're not strictly required. (We had this discussion regarding pull-ups on BOOTSEL and RESET, and maybe elsewhere too)