Myth? Kind of.
There are 2 aspects that people often confuse. If you make a change to your domain name with your domain name registrar, for example changing the name servers, that is pushed to the 13 root servers around the world. That's where the propagation comes into play. In years past, that could take hours or even days waiting for the registrar to take the information you provided, push that to their deployment servers which would update the root servers twice per day. That's improved rapidly over the years and often times changes made to your domain name take take effect nearly immediately.
On the other hand, if you make a change to your DNS zone, like adding an A record or an MX change, that should take 'up to' as long as the TTL setting to be updated everywhere. That's not really propagation though, it's caching. Microsoft DNS, for example, defaults to 1 hour TTL.
With the caching, if you happen to use the domain name just before making a change, and the TTL is 1 hour, then it will take an hour for it to be updated. However, if you haven't tested anything with the domain name just prior to the change, then your change will be immediate for you. (i.e. add a new A record that you haven't tested with yet, and it will take effect immediately).
So, nowadays almost all changes will take affect within an hour (or whatever your DNS TTL is set for). The only exceptions are if a DNS server doesn't honor the TTL (spammers often don't), or if your domain name registrar's servers aren't updating properly to the internet and you make a registrar level change. That isn't often though.