If I went into my DNS nameserver settings for my domain and changed the nameservers to the following what would happen?
myhost = the host that I'm on right now
newhost = a mirror host I may set up that will say "We're sorry, the page is down currently" or something like that
If what my friend says is true, then if myhost goes down, say a server is getting replaced or the network goes caput, the domain should automatically resolve to newhost.com servers with my mirror page.
If my understanding of DNS is right, your friend is wrong.
As I understand it, someone wants to look at your site, they query one of your nameservers (in no particular order), your nameserver provides an address for a web server, if that server is down that someone will just get a 'page not found' error or something like that
For an example of this go to http://www.DNSStuff.com and do an A record lookup for your site. Watch which name server if picks, refresh a few times and you'll see at least one time it switch to use a different one.