I would agree, but I can imagine situations in which "Do you speak English?" is a question about habitual action, without addressing ability (albeit, perhaps assuming ability). For example:

"When you and your sister visit your Uncle in Canada, do you speak English?"
"When we are around him, yes; it would be rude not to include him in the conversation."

"When you teach that English 'immersion' class, do you speak English?"
"Yes, all the time: that's the difference between the regular English course and the English immersion course."

And now, some Chinese examples, using the very line from this exercise, but sometimes specifying "can you" rather than "do you" for contrast. Imagine a Chinese actor gets a brief speaking part in an American movie being shot in ShangHai; the actor's friend is surprised, and asks the actor if he speaks English: not if he can speak English, but simply if he does speak English for that line in the movie:
你说英语吗? (Do you speak English?)
说。我在电影说英文。(Yes. In the movie, I speak English.)
真的？可是，你会说英语吗? (Really? but, can you speak English?)
不会，可是，我明白我说什么。 (No, I can not, but, I understand what I say.)
你说什么? (What do you say?)
我说，(I say,) "Give us your suitcase, Mr. Lambert!"
意思是什么? (What is the meaning?)
意思是，"林拔先生，给我们你的行李!" (The meaning is, "Mr. Lambert, give us your luggage!")
所以，你不会说英语， 可是，你说英语吗? (So, you can not speak English, but, you do speak English?)
对： 我是一只鹦鹉。(Correct: I am a parrot.)

Yes: 你说不说英语 means, "Do you speak English?" The "verb not verb" pattern is another way of asking a "yes/no" question, an alternative to the "verb ... 吗“ pattern used in this exercise.

I believe SantaRPG's point may be that if you are using 会 (hui4) to mean, specifically, "Can you speak English?" then the "verb ... 吗” pattern of that question is 你会说英语吗, but the "verb not verb" pattern is 你会不会说英语 (rather than 你会说不说英语, which instead would mean something like "are you able to speak or not speak English?" or "is speaking English or not speaking English something you are able to do)?" In other words, the "verb not verb" pattern of "Can you speak English" would be "you can not can speak English" rather than "you can speak not speak English."

When using the "verb not verb" pattern, it is important to remember which verb to put on either end of 不. In your suggestion, of course, you simply used 说 (speak) as the only verb, by itself, rather than 会说 (can speak); therefore, 说不说 would be correct, as you suggested. However, had you wanted to use 会说, the correct "verb not verb" pattern would be 会不会说.

I hesitate to say this is "always" the case, but often, when two characters form a verb, the "verb not verb" form of a question using that verb applies to the first character only:

你知道吗? = Do you know? ("verb ... 吗" form)
你知不知道? Do you know? ("verb not verb" form)