The great majority of people posting on the internet don't actually do research. They just wander around the net, looking for soneone who's done, or will do, the research for them. They accept anything and everything they read as certain, not knowing who's reporting it, and where it's coming from, and pass it on as fact, but with absolutely no idea of whether or not there's so much as an iota of truth to it!
You're to be congratulated for refusing to believe Mary died in 1813, just because people on the net say so. If you were to track the report back to it's source, you might find there's only one source; it's unacceptable, and even at that, it doesn't say what people are now reporting it said.
If Mary lived until 1876, you'll find her on the 1850, 1860, and 1870 census records, listed by name, and with her age, place of birth, and relationshuip to the head of the household, given. Start with the last place she's know to have lived, find her there, and work backwards from there.