BEDMAS where the order of Addition before Subtraction matters? Here is a recent "tricky problem" that is making the rounds on FB:

BEDMAS is explained here in a video, with this being the upshot:

Everyone understands that 6 - 0 + 1 = 7, but I was challenged to follow BEDMAS exactly (A, then S) which results on paper as 6 - 1 = 5 (because we would apply 0 + 1 first).
I tried to explain it as 
6 - 1 x 0 + 2 / 2 = 
6 + (-1) x 0 + 2 / 2 =
6 + (-1 x 0) + (2 / 2) =
6 + 0 + 1 =
= 7

But alas, adding a sign, the other party was unconvinced (and very smug). 
Question: How to justify to a non-mathematician that the answer is in fact 7 following BEDMAS? Or is the above the only way?
Research: This question was very similar, but the resolution hinged on a grouping mistake and isn't applicable here.
Note: I thought about posting in Math Education, but this leans more towards a proof, I suppose.

"A, then S" is a misunderstanding of what BEDMAS stands for.
The priority of operations is as shown in the video:
Brackets/parentheses 
Exponents 
Multiplication/division 
Addition/subtraction
The reason addition and subtraction are listed on the same line
is because they have the same priority.
Notice that they didn't even bother to list multiplication and division
in the same order on the line as they occur in the acronym,
because it makes no difference.
I somehow managed to make it through the U.S. math education system without
having been scarred by the use of these acronyms, so I can look at them
and figure out what they mean based on how standard arithmetic
really works, rather than the other way around.
