This is true for a wireless router but not for an adsl wireless router. The names are confusing. Basically you have 2 types, one with a built in adsl modem (and include "adsl" in the name, the other without a built in adsl modem (but often called "dsl" routers. (no "a"))
What you want is an adsl wireless router such as the Belkin F5D7632UK or Netgear DG834G, both of which have built in adsl modems.
The advice you read fails to mention that having a seperate adsl modem connected to a seperate router can be a nightmare to configure, whereas the built in adsl modem types are easy.