Positioning on the field and proximity to the 1st Tennessee by the 27th Tennessee. Also, most maps of the field are off some. Jamie Gillum, who has written the best book on Spring Hill on Hood's TN Campaign, is also the author of the unit history on the 16th TN (3 volume set) as well as a book on the 16th TN at Perryville and he told me about a map that had been found while Kurt Holman still ran the park that proved that most maps were off - and this was also used to offer the idea that the flag was that of the 27th TN.
Having seen the Polk Corps flag in question in person many times, both in Wisconsin and at the TN State Museum when they had it, there are few holes in the flag - certainly would have been more it it had been the flag of the 1st TN since they attacked a Union battery firing canister!
Having said all of this I know that some think that the flag is that of the 6th TN as well but Jamie and Kurt lean heavily towards the 27th.