It seems that you just never know what a mortgage company might do. In 1997, I bought a new double wide mobile home and let the dealer arrange financing since he could get me a better interest rate than my bank or credit union. A couple of years later, some outfit I had never heard of in Florida offered to refinance it at a lower interest rate. I called the company that had the financing already, and instead of "refinancing" they just lowered my interest rate and sent an "addendum?" to the original contract.
We bought this house 6 years ago and because of some uncertainties at the time, I went with a 30 year mortgage with 20% down and cash for all the closing costs. Prime Lending arranged the mortgage at a tenth of a percent less than my credit union wanted, i.e., 5.75%, and a lot less trouble. I knew the mortgage would be sold to some bank, and it went to Wells Fargo. Of course I've been paying a little extra each month anyway, but a year ago, they called and offered their in home, no cost, refinancing, with several options, if I was interested. So I went with a 15 year mortgage at 4.125%. Now I know I could have beaten that interest rate a little bit, but there would have been closing costs, appraisal fees, etc. The refinance and a complete new mortgage with Wells Fargo was done at no cost to me, except what I paid a notary. Wells Fargo even paid the shipping costs both directions for all the paperwork.
Like you, I wasn't looking for lower payments (one of the options they offered), I was looking for shorter term and lower interest rates.