So, just to make it clear...there is no law that required Sam Adams to misquote the Declaration of Independence.
Nor would the "Beer Institute Guidelines" have applied, as this is a direct quote from an American Historical Document.
Sam Adams Beer choose to amend the quotation for their own reasons, whatever they were...
...and they are responsible for the ramifications of that decision.
NO, there is no "misquote"
because they're not quoting it and it is the height of idiocy to pretend that that's what a beer commercial is.
Paraphrase
Definition:
A restatement of a text in another form or other words, often to simplify or clarify meaning
What Fox Noise and Whirled Nuts Daily are doing is playing the part of the
Unreliable Narrator:
>>
The nature of the narrator is sometimes immediately clear. For instance, a story may open with the narrator making a plainly false or delusional claim or admitting to being severely mentally ill, or the story itself may have a frame in which the narrator appears as a character, with clues to his or her unreliability. <<
And obviously, if we're bending over backward to pretend what we're hearing is a verbatim quote from the DofI and complaining that a part is missing, then just as obviously, it's NOT a direct quote from a historical document. Not that that has any bearing on the marketing guidelines anyway; if the guidelines say no religious icons,
then you don't use a quote that contains one.

The marketing guidelines say nothing whatsoever about "unless the material is a direct historical quote". That's completely irrelevant.
You're trying to have it both ways here: first a complaint that it's a misquote, then a complaint that it's a direct quote. Pick a side.
Beer commercials are not historical documents. They are marketing tools. The Unreliable Narrator lies with his false premise that to use phrases that exist in the DofI automatically means the entire text must be used. So let's cut the bullshit. That isn't what the commercial was doing and never was. False premise, ergo point is complete bullshit.
Moreover, what business is it of Fox Noise, or WND, or us, to declare that a private company must invoke a deity in its marketing? Why is Fox Noise taking the side of authoritarian theocracy here?