Well I'm not official but I can give you two defenses to rebut your GM.
The Grammar Nazi rebuttal: The "They" that your GM is citing as referring two weapons is in a different sentence from the mention of two weapons. As the subject of a new sentence, the ambiguous pronoun should be referring to the subject of the paragraph, which any high school student can tell you is "Automatic Weapons".
The Rules Lawyer rebuttal: Any good rules lawyer cites precedent. There's a lack of precedent to support Semi-automatic bursts applying only to two weapons. For example, the rules for Semi-automatic bursts that follow the disputed rule fail to account for how to handle two weapons. You expend 3 rounds... it doesn't say which gun has to fire the extra bullet. At the same time, the plain language involving Semi-Automatic Bursts "clearly" describe single weapons in context. For example, consider the rules for the alternate Semi-Automatic Burst called "Double-Tap".
A rapid pair of well aimed shots from a Semi-Automatic-capable weapon fired in such a way to increase damage instead of making it harder to avoid.
It's both explicitly saying you can perform this kind of burst with a singular weapon, and implicitly is confirming that you can perform it in place of a single weapon performing a semi-automatic burst.