When users access a Boosted server, they get a password prompt
The web browser make a decision whether the site being accessed is a trusted site or not. Intranet servers will be trusted if the host name does not contain dots (eg http://myserver instead of http://myserver.myco.com/ ) or the host appears in the browser's list of trusted hosts.
In Internet Explorer: Tools > Options, click the Security tab. Next click Sites then Advanced. Add the server(s) in question. See attached. Note that you are able to use an asterisk for the server name, eg "http://*.myco.com" instead of specifying every server individually.