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.

To be honest, I never thought of BEDMAS or all other acronyms Americans seem to use.
Instead, I try to teach my students that some operations are "stronger" than others, and thus have priority: for example, powers are done before multiplications, and multiplications are done before additions.
Adding and subtracting have the same priority, just like multiplying and dividing, because they really are just the same thing.
