Will an assumption make me responsible for the mortgage?

I just talked to our home loan Bank with a request in regards to putting the house in my name but not assuming responsibility for the mortgage. I just put my parents in a nursing home and I cannot afford the mortgage payments. They told me I have the option of what is called "simple assumption" with a claim that I can put my name on the house but that they cannot come after me if the mortgage payments are not made. While on the phone with the representative, I googled simple assumption and the websites I found said something quite the contrary. I told the woman, she put me on hold for about five minutes and when she came back on I asked her for a link to their website which would provide more information on simple assumptions. I told her that everything I found on the net stated that they could come after me. But she insisted that they wouldn't according to their policy.

I'm taking this as a red flag that they're trying to sweet talk/deceive me into assuming responsibility for the mortgage. Now they're sending me a simple assumption application form which I have to pay $100 to have processed. In the meantime the house has to be put on the market by the 31st of September according to the county which has provided medical assistance for my parents. They plan to put a lien on the house but I have the option to put in my name because I have cared for my parents for over two years. If the house sells I could stand to make a profit but with the economy being so bad it could sit for several years and the money invested in keeping mortgage afloat would be wasted.

If you know anything of simple assumptions and can link me to information on the do's and don'ts, I'd very much appreciate it. this is truly an 11th hour situation-So any help would be greatly appreciated.