Where does the argument that people have been around for at least 100,000 years or more come from? Is there any truth to it?

It comes from the argument that the earth is billions of years old and that man was the result of random elements and chance. If that is assumed, then man—or, better said, man-like creatures, would make sense to be 100,000 years old, or older, the processes of evolution needing so many countless years to move to the level of sophistication evident in homo sapiens. This would also be the conclusion of so-called “old-earthers,” who equate the yom (Hebrew word for “day”) to represent epochs of time versus specifically literal 24-hour days. In the case of “young-earthers,” you do translate yom as a 24-hour period of time, in which case you have the creation of mankind occurring with divine process: Then God said, “Let us make man in our image, in our likeness, and let them rule over the fish in the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground.” So God created man in his own image, in the image of God he created him; male and female he created them. . . . [T]he Lord God formed the man from the dust of the ground and breathed into his nostrils the breath of life, and the man became a living being. . . . So the Lord God caused the man to fall into a deep sleep; and while he was sleeping, he took one of the man’s ribs and closed up the place with flesh. Then the Lord God made a woman from the rib he had taken out of the man, and he brought her to the man. The man said, “This is now bone of my bones and flesh of my flesh; she shall be called ‘woman,’ for she was taken out of man.” For this reason a man will leave his father and mother and be united to his wife, and they will become one flesh—Genesis 1:26-27, 2:7, 2:21-24.
What must be borne in mind is that “young-earth” versus “old-earth” is not a salvation issue. I fully expect to see “old-earthers” in heaven, because what places us in heaven is Jesus Christ placed in us. What has historically happened, however, is that Christians over time have tried to accommodate what they viewed as the seemingly strong case of evolution into an amalgam which features the processes of evolution with the divinity of God superintending it all. He basically provided the ingredients and then let nature take its course. One danger of this, of course, is that it removes the miraculous, the instantaneous, out of the picture. A “young-earth” position arguably grants God all power to do exactly what Scripture seems to indicate: God said . . . and it was so. As the Son who was present at creation would say so many centuries later, [A]ll things are possible with God—Jesus Christ, Mark 10:27b. A second danger is that it removes God from the intimacy with which He created the world and continues to oversee the world. It moves God into a much more “deist” position, meaning that God basically provided the ingredients to make everything and then spun it all off to fend for itself. Again, this seems to contradict Scripture which presents a God intimately involved and connected to all the details and goings-on of planet earth. As God Himself said through the prophet Isaiah, Though the mountains be shaken and the hills be removed, yet my unfailing love for you will not be shaken nor my covenant of peace be removed—God speaking, Isaiah 54:10a. And of course, the final words Moses gave to Joshua just prior to Israel’s entrance into the Promised Land serve to remind us of the ongoing, unbroken faithfulness that is ours in God through Jesus Christ: The Lord himself goes before you and will be with you; he will never leave you nor forsake you. Do not be afraid; do not be discouraged—Moses, Deuteronomy 31:8. And those same words, reflecting that same sentiment, continue with us through Christ Himself: And surely I am with you always, to the very end of the age—Jesus Christ, Matthew 28:20b. God’s words, and His actions, reflect His character. He created based on that same character. He didn’t create the earth to run itself. He created the earth to have fellowship, and be in relationship, with Him.