I believe I noticed a discrepancy on the documentation for updating a record.
The returnFieldsByFieldId parameter is not specified as being an option on the Request Body, but it is mentioned in the Response Format section. It's also mentioned in the description for the endpoint too.
Unfortunately, this parameter is not currently supported when updating a record, however I would love it if it were!!
See this screenshot:
Please consider adding support for returning fields by IDs when updating a record, so your documentation will be accurate 😉