Many many years ago changes at your registrar to your DNS settings took 24 – 48 hours.
The Internet of 2016 however is much faster. Yes, DNS wlil take time to hit ever DNS server on the planet, but if you change your nameservers for example and you’re hosted in the USA you can expect your DNS changes to be seen on networks across the country in about 30 minutes.
I’m not sure why all the big companies keep repeating this myth, but they are all wrong. 🙂