I was told the same thing by my midwife at a hospital.
As I wrote out my birth plan, mostly for myself since everyone there pretty much laughed at the idea, I figured out why I really didn't want EFM or a needle in my arm. I'm not relaxed at either idea, so why, during the one time in my life when everyone is basically trying to get my body to relax, would I do those things?
It takes less than 3 seconds for a well trained nurse to put an IV needle (locked or flowing) into the arm of a healthy woman. I'm perfectly healthy, and they hardly need 3 seconds 99.99% of the time.
EFM has been shown to have no added benefit to mother or baby, even the ACOG says so. Because we don't know enough about what the results mean to actually apply them to real life. Continuous EFM increases your risk of having a medically unnecessary cesarean by 30% (more if the nurse isn't trained).
Even at the hospital, I have certain human rights that should not (legally) be violated, and that includes informed refusal of non-emergent care. EFM, needles just-in-case, and even vaginal checks all qualify as things I can, with enough documentation up front and a doula and hubby and loud hassling, refuse consent to. But if I want to give birth at a hospital, sadly, I will have to fight for those rights every single step of the way, which ALSO isn't relaxing.
Just my thoughts.