One measurement cannot tell you if you are measuring big. Most care providers would say that normal at 35 weeks is to measure 33-37 cms, and not until you are more than 3 cms difference, on consecutive visits, are you outside of normal.
Measurement doesn't always equal size of baby. I measured just 1 cm over with my 10+ lb baby, and 2 cm under for my 8.5 lb baby!
You are probbably not more likely to birth early based on size alone. Measuring large can be your caregiver's mismeasurement, lots of fluid, a baby high in the pelvis, and just plan normal for you. Fundal height measurement is just one tool in confirming normal, or exploring other possibilities, and is not super-accurate in detecting abnormal, but is not particularly obtrusive and can pick up growth differences.
As for ruling out a homebirth, that is something you need to explore further with your care provider. I assume more measurements and palpations will be done, and you can discuss with your care provider what is found, what his/her thoughts are, what your thoughts are, and come up with a plan. But automatically? Not in my books-- just another consideration in the whole picture.