Your observation is correct on loans that are not assumable. The technique--which some investors use--is called "subject to." That is, you acquire the home "subject to" the existing financing. The mortgage(s) stays in the name of the original owner. The deed is transferred to you. At some point, you'd refinance the property, thus taking the mortgage out of the seller's name and getting a mortgage in your own name.
The process is quite safe for you, but risky for the seller. If you default on payments, the lender will come after the seller--not you--since the mortgage remains in the seller's name. However, as you noted, a "subject to" transaction would allow a lender to trigger the "due on sale clause." As a practical matter, in today's economic environment, that's pretty unlikely.
Hope that helps.