Very Weird Large Cent

Alright, so, before y'all flip your brains, I'll try to get pics later. But for now, descriptions may have to be it. While my dad and I searched through an inherited coin collection, we found this wired large cent. The "large" cent was about G4 condition, but the weird thing about it is that it isn't large at all. It is the exact same diameter of a Flying Eagle cent, and shows no signs of being ground down. I know there are high suspicions of it being ground down, but my reasoning is this: Back in the 1860s, when these were still commonly used, a cent was worth a lot more than today. Furthermore, power tools were very limited or non existent back then. Even if they were widely available, who in the world would grind down their paycheck? Fast forward a hundred years, when power tools are more common, these coins would be worth at least $5 apiece, and a rare find. If someone were determined enough to grind down a large cent in the 60's, surely there'd still be marks on the edge of the coin. I know this didn't happen though, because my grandpa (the original owner of the coins) worked as a bank teller, which is where he picked these out of circulation (this was in the 1940's). Surely he wouldn't have picked them out of circulation only to damage them afterwards. The only possible thing I can think of that would have caused this is this: My grandpa was going through coins at the bank, picking out the interesting ones here and there. He may have then saw this, assumed it was a small cent that looked weird, and picked it out. But, back to the previously mentioned problem: power tools were not common back then. I gladly accept all opinions. Thanks.