It had been becoming clear to observers that the scoring rule change, and the voluntary budget cap for 2010, was part of the wider political battle over the future of the sport.
In implementing the 'gold medals'-style system championed by Bernie Ecclestone, the FIA seemed to have deliberately ignored FOTA's separate proposal, where the points difference between first and second places is simply increased from 2 to 3 points.
"FOTA had made a proposal that was carefully based on the results of a Global Audience Survey, which allowed listening to preferences of the public, and all the Teams firmly believe that these indications should be properly taken into account," the teams' Friday statement read.
FOTA also claims the rule change contravened Appendix 5 of the Sporting Regulations and article 199 of the International Sporting Code, where it is "too late for (the) FIA to impose a change ... that has not obtained the unanimous agreement of all the" teams.
In its own subsequent statement, in which the FIA suggests that Ecclestone "had been told that the teams were in favour" of the gold medals scheme, F1's governing body backed down.
"If, for any reason, the formula one teams do not now agree with the new system, its implementation will be deferred until 2010," the FIA said.
FOTA said the teams are willing to "collaborate with the FIA" for a jointly-defined new points system for 2010.