Oh, I'm sorry! I misinterpreted the verb, "has" in your first sentence and didn't take the second one into consideration! Now, I re-checked the link you provided and found and read some more examples on Google.
First, let's talk about "There is no question but what". One of the examples I found was:
"MR. MCCORMACK: I take it that the effect is different upon different persons.
DR. MUNCH: Yes. sir.
MR. MCCORMACK: There is no question but what this is a drug, is there?
DR. MUNCH: None at all.
MR. MCCORMACK: Is it a harmful drug?
DR. MUNCH: Any drug that produces the degeneration of the brain is harmful. Yes; it is." (
Source)
The underlined tag question (asked by Mr. McCormack) and then, Dr. Munch's answer in the following line may help us to find the meaning of the expression. Considering them, it seems that "there is no question but what" means "there is no doubt that".
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And about "There is no question but that", I found this description in the 3rd paragraph of
this page:
"
...The insertion of but before that, as in “I doubt but that” and “there is no question but that,” makes a double negative that is probably full-blown. Nevertheless, as we have seen, it is heard on the floor of Congress every day, and the Fowlers show that it is also common in England."
And this is an example of how this expression is used (
Source):
"
There is no question but that City of London School for Girls is a high-end school. Fiendishly competitive admission (10 girls try for every one place), teamed with challenging teaching and the expectation that girls entirely immerse themselves in their subjects before exam time, produce some pretty startling results."
In my opinion, the 2nd and 3rd sentences explain the reasons for which City of London School for Girls is a high-end school. Therefore, again, "There is no question but that" means "there is no doubt that".
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Hence, the conclusion could be:
There is no question but what = there is no question but that = there is no doubt that
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RECENTLY ADDED: I HOPE NATIVE SPEAKERS TELL US WHAT THEIR OPINIONS ARE.