You are absolutely correct.
CALIFORNIA CODE OF REGULATIONS - 2 CCR § 5025
"(b) Short time parking zones when designated by painted curbs shall be green and stenciled with the time limit allowed for parking. No person shall park any vehicle adjacent to a curb marked in green for any period in excess of the posted time limit."
Here are some examples of city/county ordinances regarding green curbs.
Long Beach Municipal Code § 10.26.010
"C. Green indicates parking limited to a time from ten (10) to thirty (30) minutes, as determined by the City Traffic Engineer for a particular location or locations, between 9:00 a.m. and 6:00 p.m. of any day, except Sundays and holidays. A legend containing the applicable time limitation followed by the words "MIN. PARKING" SHALL be stenciled on the green, OR appropriate signs may be posted."
Monterey City Code, Chapter 20
"Green Zones: Short term parking, to be used for 12 or 24 minute parking only. These zones are clearly marked by a green curb and/or a sign. The time limit will be specified either on the curb or the sign."
Sacramento County Code § 10.24.010
"Green curb marking means no stopping, standing or parking for a period of time longer than twelve (12) or twenty-four (24) minutes, as designated by signs at any time between 7:00 a.m. and 6:00 p.m. of any day except holidays and Sundays."
This is not true. See the local ordinances above.
This may be true for some things but not when it comes to green curb time limits, they must be posted.