Anything is possible, including the possibility the abductor wanted to feed her to his pet tiger.
In your scenario, the 14-yo ran off with her driving-age boyfriend, and the little sister is making up a story to cover up what she knows, so that "true love" can bloom. A fake abduction is a bit melodramatic, and not your likely elopement scenario. But if the little sister's making it up, we'll know soon.
Far more likely that the abductor is a pervert who saw her somewhere, followed her home, and took his chance at grabbing her. That'd be very bad: she's probably dead by now.
And I dont think the sister is making up the story. I think the missing sister gave her the story and instructions on when and how to tell it.
1) The kidnapper would have had to see her far earlier in the day. Unless she was out playing in the streets closer to 2 AM.
2) He would have after seeing her had to follow her home and determine that it was her place of residence.
3) He would have then had to return to the home and break in without anyone waking (that is very possible)
4) He would have then had to manage his way directly to the girls room, making no mistakes and not entering the parents room by accident. (leading me to believe he knew what room to go to)
5) Upon entering the room and surprising the girls with his presence they would have had to remain silent from the get go. (Now who is going to wake up to a man with a gun in their room and not scream, especially a young girl, 2 of them!)
6) He would have then had to make his way out of the home with the girl putting up little to no struggle thus not awaking her parents.
7) The younger sister would have then had to sit there for 2 hours, silent, not fall asleep and then proceed to her parents room to tell them what happened. (I would think, if this actually happened she would not have waited 2 hours, though it is a very remote possibility.)
I am leaning very heavily toward her running off with someone she met on line, or a boyfriend. Though I have moved decidedly toward the online option.