Beyond 习惯 a general “framework” desired for 得's uses in “主语”“动词” 得是什么?, “主语” “动词” 得是鸟语，“主语” “动词” 得 “名词,” et cetera Concerning the use of 得, which in my text below is to always be pronounced using the pinyin romanization “de,” after a verb I am familiar with the structures

A: “Subject verb 得 (adjective transformed to adverb)” like 他跑得快 and 

B: “Subject verb 得很 (adjective transformed to adverb)” like 他跑得很快,

as well as potential complements like

C: 听得懂 and

D: 办得了 (bàndeliǎo).

But the following structures E-H using 得 don't match more general forms of any of the above structures A-D. --Please consider them.

E:  她说得不是, in which 不是 （bùshi) in this case is a noun with a different pronunciation from búshì that one might expect if 是 (shì) were otherwise far more commonly used as a verb.

F: 讥笑听话的人不懂对方说得是什么。 (http://digchinese.com/en/saying?page=2635 on the Internet).  After talking with a native Mandarin Chinese speaker I think the meaning of this sentence could be more obvious for a Westerner learning the Mandarin Chinese language with a good Mandarin Chinese-language dictionary if it would instead be written as （某人）讥笑听话的特定人不懂对方说得是什么 or   （某人）讥笑听话的那个人不懂对方说得是什么 or（某人）讥笑听话的人，他不懂对方说得是什么 or （某人）讥笑听话的人。---他不懂对方说得是什么。

G.  …..或是说得是鸟语 (http://www.google.com/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=2&amp;cad=rja&amp;uact=8&amp;ved=0CCsQFjAB&amp;url=http%3A%2F%2Fwww.zhangxinxu.com%2Fwordpress%2F2012%2F05%2Fhtml5-speech-x-webkit-grammar%2F&amp;ei=xMlKVKvvA5S3yASP34KIBQ&amp;usg=AFQjCNFdv1IUDPNtUUcugEhhTFyA069k4Q&amp;bvm=bv.77880786,d.aWw), with help from a native Mandarin Chinese speaker meaning “perhaps what (he or she?) says is bird's language,” so is nonsense for human beings.  (I understood from a native Mandarin Chinese speaker that this would be very impolite speech because it would be talking about a human being like he is a bird, which he or she is not!)

H.  你说得是什么？ With help from a native Mandarin Chinese speaker I think this means something like “You say what?” or “What do you say?”.  I think this is a very commonly used interrogatory statement among native speakers of the Mandarin Chinese language.  So I think it could be a good, yet short example of the sort of sentence structure I want to discuss here.  Note the difference between this question and the question using 的 instead of 得of 你说的话是什么？.  I suppose that 你说得是什么？and 你说的话是什么？would have the same meanings.

Question 1: May I regard the above structures E-H as more general forms of the above structures A and B in which a noun or the pronoun （代词）什么following “verb 得”can replace an adverb (副词)  following “verb 得”?  If so, this might be the simplest way for me to accept an understandable “framework” for structures of the forms of A, B, and E-H.

Question 2: May I consider all of the structures A-H generally as complements (补语) with the cases C and D considered as particular types of complements called potential complements?
@user58955 is correct. Example E to H are wrong usages of 得, they all should be 的 instead.

E. 她说的不是。 What she said is not. (This is a bad example. As you can see in the English translation, something is missing here.)
F. 不懂对方说的是什么。 Doesn't understand what the opponent says.
G. 你说的是鸟语。 What you said is lingua avis.
H. 你说的是什么？ What is it that you said?

The pattern is obvious.

Now let's take a look at example A to D:

A. 他跑得快。 He runs fast.
B. 他跑得很快。 He runs very fast.
C. 听得懂。 Listen get understood.
D. 办得了。 Do get done.

Notice in these 4 examples, 得 acts as a connecting device between the verb and the status or result of the verb. Also notice that the weight of the sentence is on the status or result, 快, 懂, or 了. This is how you use 得 to form complements. In a sense A, B are only slightly different from C, D in there specific purposes, but the major function is the same.

Example A and B -- You wouldn't call the English counterparts complements, do you? But remember I talked about the weights. If the weight is on the modifier, the modifier would be considered as a complement. If you want a non-complementary adverb, you need to use this form:

他飞快地跑。 He quickly runs.

Now the weight is on the verb 跑, and 飞快地 acts 状语 instead of 补语.
Example C and D -- There just isn't an English counterpart. This might be why it's confusing you and making you think it's special. It's not. You just have to think the Chinese way.