I can see why you're skeptical and if it does in fact run into issues, they will replace the whole phone. I know this because I was in that predicament. When they replaced the screen, everything was fine and dandy, sorta of. One minor issue I noticed was that when touching any part of the screen, mostly in the center, you can see pressure points on the LCD as if you are touching the display directly. I wasn't happy, but I was willing to let that slide. What ticked me off was when I got a new case on my phone, it didn't "hug" the screen as tightly that when I tapped the display, it sounded as if it wasn't adhered to the body on the phone correctly that it made a clicking noise. Like there was a slight gap between the display and the body. Upset, I made another Genius appointment, and they replaced it without hesitation. I was worried I wasn't able to replicate the clicking that I threw in the issue with the pressure on the LCD while touching the phone, but the Genius held it up to her ear, and said it's very slight but I'll replace the whole phone.
So long story short, if they do in fact replace just the screen, they will replace the whole phone the second time around.