规规矩矩: 国语 vs. 普通话 (Taiwanese Mandarin vs. Mainland Mandarin) 规规矩矩 seems to have two - not so agreeing definitions in guoyu and MSM.

The MSM definition looks something like this

规矩 - 互动百科


  2、[Well-behaved；Well-disciplined；Remain orderly；Have proper 
  behaviour] 引申为称人的品行方正，谨守礼法
  
  靠右的一间正屋住着屋主罗斯托玛乞维列，一个规规矩矩的市民。——《第比利斯的地下印刷所》
  又如：没规矩；守规矩


品行方正, 谨守礼法 equates to something along the lines of upright and upstanding.

The Taiwanese Guoyu definition from the Ministry of Education:

MoE


  形容行為有條理、有次序, 合於法度。


有條理、有次序 - orderly / organized / prioritized

合於法度 - legally

Guoyu seems to have the idea of orderly and organized where MSM doesn't. 

Are my asusumptions correct?
規矩 doesn't mean exactly same as 規規矩矩. I don't quite agree how MSM uses 規規矩矩 to explain 規矩. 規規矩矩 and 規矩 share the same core meaning, but translated differently in different part of speech. In a nutshell, 規矩 =/= 規規矩矩, 有規矩 = 規規矩矩. 


規矩(n) - regulation, plan, rules, scheme, discipline,etc.
That's why when you want to say something is well disciplined you say 有規矩, it literally means "it has discipline".  You need a adverb or adjective if you want to translate "well disciplined" literately.  
規規矩矩的(Adj) - regulated, planned, ruled, well disciplined, ordered, legal, etc.
規規矩矩地(Adv) - regularly, orderly, legally, etc.
As you can see 規規矩矩 has more meanings simply because it functions differently in a sentence. Since "well disciplined ~= do sth in order = orderly", 規規矩矩 seems to have more meaning than simply 規矩. Keep in mind that "orderly" has a different meaning from "order", though in English they share they same root, in Chinese "order' would have translated differently to for example 次序. 


I know my answer is quite messy but hope it helped.