For complicated reasons, this can happen when hydrogens are adjacent to a stereocenter, a concept that was not covered in the chapter. I have chosen to talk in class only about a fixed magnetic field and changing the RF frequency for the sake of simplicity. I hope this can clear up at least some of the confusion. That is correct. If a hydrogen atom's nucleus is more shielded wouldn't it have more electrons around it thereby requiring more energy to flip the spin.
Electrons shield the nucleus from an external magnetic field.
The more electron density around a nucleus, the more shielded the nucleus. More shielding means that the nucleus underneath feels less of a magnetic field, thus less energy is needed to flip a spin. I know this sounds weird, that one magnetic field induces an opposing magnetic field, but it is true. The nucleus would feel the entire magnetic field, thus is would take a larger amount of energy to flip the spin. The more electron density around the nucleus, the more shielding and the less energy required to flip the spin.