This is absolutely not true. The only incoming students guaranteed any kind of funding are the three receiving "recruitment TAships." If you are not one of these, and you do not receive an RA position through your advisor, then you probably will not get any financial assistance through the department. Also, you are not guaranteed any funding for any length of time (i.e., at least 3 years). Although there are loopholes, usually you are in "Tier 1" (the Tier where funding is most likely) for about 4 semesters. After that, you will typically have to find your own means of income outside of the department. Considering the department routinely takes in far more students per year than confers degrees, I suspect that the length of time a student will have in Tier 1 will continue to drop as student enrollment increases....that or there will not be enough TA positions to offer to everyone in Tier 1.
Remember, this is a huge program (~80 graduate students). The fight for funding is highly competitive, and after you have used your TAship semesters, you will be competing against students who have been here 7-14 years already and have preference for other funding opportunities. Outside of the TA positions and those opportunities that come through your advisors (i.e., RA positions) the odds are very much stacked against students early in their career, regardless of academic standing and teaching background. If you are in the biological subfield, you will have an even more difficult time finding help in this department, as the administration in this department have interests heavily weighted toward cultural and archaeological studies. Unfortunate (given the remarkable accomplishments of the biological staff), but true.
One last thing to keep in mind with regard to cost- if you are out-of-state, you will always be out-of-state. While many schools allow you to apply for in-state residency after one year, UMASS does not. The only way you will ever become in-state is if you can prove you moved to Massachusetts for some reason other than to attend school. Keep this in mind, as Amherst is a very expensive place to live, and the average length of time to get a PhD in this program is almost 11 years (longest in the whole university). This means that odds are good you will have to take out loans for at least a few years, and the loans will not be enough to survive off of without at least another part time job- trust me!
I know this might all seem like a downer, but I feel it is important that someone tells you this before you accept a position here.