I would suggest having a load of
wood chips brought in. fill that boggy swappy area with them
They can be replaced when needed and with break down adding nutrients to your soil.
I feel what your neighbor has suggest is a lot more work and maybe other problems.
My neighbor repaired an area like that by burying big rocks. It worked though it was a lot more work than a load of wood chips. Unfortunately we cannot get wood chips here unless we make them ourselves.