For T-Mobile, the above is true but don't be mislead. This (roaming) applies only in areas where T-Mobile doesn't have any towers at all; if T-Mobile had nothing in Oshkosh, for example, then they would cut a roaming deal with another carrier until such time as they are able to install (or justify) their own tower.
Where roaming DOES NOT apply is in the case of you have T-Mobile in your general area but the signal within your home, office, grocery store, whatever is weak to non-existent. For example, I have great T-Mobile signal in my office parking lot but zero within my office. Even though there is passable AT&T signal in my office, I cannot roam on AT&T while inside. I called T-Mobile about this and was told what I described above.