An oil company or landman likely does find who actually owns the property (unless the title is clouded.) What they don't know is who inherited it. They would contact the heirs but that presumes they can locate you but often landmen are pretty good genealogists. Filing the affidavit would create that title continueity. As for leasing you, the landman would need to want to lease that land first, then they would contact you about leasing.
Unfortunately, too many companies have developed bad habits...blanket leasing anyone who is near the property often on the basis of bad titles. Now they are trying to fix those titles and, if the Fayetteville Shale play is any indicator, the courts are clogged with title suits. Chesapeake Energy was notorious for leasing anybody walking then trying to figure out if they really owned the land or not.
Making sure your title can be found and you personally can be located is your best defense.
I can give you an example of why title gets important in my own family. My grandfather left Colorado in 1939 and sold the surface to his brother. He kept ½ the mineral rights and only his name appeared on the deed that conveyed the reservation. In 1975 grandfather died. In 1980 grandmother died but in the interim she had signed a lease on that mineral. In 1980 when an oil company looked at the lease, they realized grandfathers signature was not on the lease. The "fix" was to sign that affidavit of heirship and no probate was done. Same for my father and uncle. They simply did the affidavit and checks were then sent to them.
My late brother (a banker), me (a geologist/appraiser), and my cousin (a CPA) realized the lack of clear ownership would be an issue someday, but dad and uncle didn't think us "young people" (we were all over 40 by then) knew what we were talking about. We literally had to wait until both died. The year my uncle passed away and both my aunt and mother were in agreement, we had to probate all of them...then created a family partnership. The check was then divided equally between my mother and aunt. (in reality each child had the rights to a portion, but our decision was for our mothers to benefit during their lifetime. It literally was the difference between my mother living in her own home until 4 days before her death and living in an apartment...and my aunt also lived in her own home up until the last 30 days of her life.)
Upon each passing, the checks are cut proportionally to the heirs, a return is filed with the IRS and the proper K forms are sent to each heir. This will never need done again. Ultimately, without such management, or something similar, the pie (which typically shrinks over time) gets cut into smaller and smaller slices and the paperwork gets unsurmountable.
Another word of caution. I mentioned my grandfather split the minerals with his brother. His brother's children inherited exactly the same amount of mineral rights as my father and uncle. There were 4 of them but they had an adjacent tract which doubled their mineral holdings. One one of the 4 retained their share. The other 3 sold. One admitted to me he sold his for $2500. I groaned and he confessed he didn't even think about calling me (even though he knew I was a geologist) Today, had he retained that interest, his share would be about 80% of that $2500 PER MONTH...and it is a very long term field with an additional 40 years of reserves.