My source for her birthplace as Ohio was an email from a third researcher - a source, but obviously not a primary source. Because I didn't know where this researcher had received their information, I began to look at what I did have on Mary.
According to my database, Mary was the daughter of Godfrey & Elizabeth (Kimmer) Heck, and had married William Shaw on August 29, 1822 in Brown County, Ohio. William died in Madison County, Indiana in 1849 and Mary died August 12, 1890 in Madison County, Indiana. Both William and Mary are buried in the Prewitt Cemetery in Pipe Creek Township, Madison County, Indiana. I have been to their graves and have posted photographs at FindAGrave for both of them.
Ok, so far I had a source for Mary's death date and birth date - her tombstone states that she died August 12, 1890 aged 87 years, 4 months and 27 days. If this age is correct, then subtracting backwards would give her a birth date of March 16, 1803. However, that doesn't give me the birthplace.
Noticing that I didn't have the 1850 census record sourced for Mary, I began browsing through the records until I found her - in Jackson Township, Madison County, Indiana. There I found her listed as a farmer with a real estate valued at $1500, born in Kentucky. All of the known children were living with her, exact for oldest daughter, Elizabeth, who had married Daniel King and was living right next door.
Ok, so now at least I had a source - whether or not this is the best source remains to be seen, but it is a starting point. I'll need to check other census records, etc. to see if I can collaborate the birthplace of Kentucky. Notice that daughter Elizabeth (Shaw) King is listed as being born in Tennessee because the census taker made a 'ditto' hash mark - under the Tennessee birthplace given for her husband, Daniel. This opens a whole other can of worms because I've seen other records for Daniel that place his birthplace as either Ohio or Indiana.