Do you need an instrument rating to fly in IMC in Class G airspace?
In the US, an appropriate instrument rating is needed to fly when WX conditions are below VFR minimums, and at night for SVFR.  14 CFR 61.3(e)

Additionally, one needs an appropriate instrument rating to fly under an IFR clearance when in controlled airspace, regardless of the WX.

Notes: ATP and things like a category and class in an airship are exceptions. Also an airplane instrument rating works in gliders. Etc.

Addendum: Specific to the OP's citing a NTSB report, the following comment is added: To rely on the mentioned NTSB report, it is important to read the findings, and understand that, a.) the pilot intended to hit VFR conditions before 700AGL and upon entering controlled airspace, b.) the pilot told people he was taking off despite qualified observers noting 200 ft clouds, c.) the airport where approach was based said they were below IFR, which would leave the pilot few options if he needed to land nearby. Given that, it is easy to agree with the NTSB. Just because something is legal, doesn't mean it is best practice, and in this case it is likely the pilot did not do as stated.

One final point, IFR without a clearance in Class G is a decision which should not be taken lightly. Years ago, I routinely did it, and the airspace was uncontrolled at safe IFR enroute altitudes.  Departing a Class G airport, with less than VFR conditions, and expecting VFR before hitting controlled airspace at 700AGL is dubious. The vest majority of my IFR flights in uncontrolled airspace, that were without benefit of clearances, were where there are large areas of uncontrolled airspace, and safe IFR altitudes could be flown enroute. Furthermore, while ATC did not issue clearances for flight in uncontrolled airspace, coordination with ATC where possible, and also with local FSS were done. That is different from popping off an airport that is likely IMC, and stating that one intends to climb into VFR weather before hitting 700AGL and controlled airspace. The frosting on the cake is having the field in the area be below IFR limits for approaches.  Good judgment is hard to legislate.