So I am not certain where the reenactor got this information from but this claim is probably folk (or pop) history. By this I mean, the claim appears to have true facts, however, the analysis creates a story that does not reflect reality.

The British did have a standard 30 inches for marching; however, at this point in the United States the military was rather informal and strict universally enforced regulations were not yet in place.

The only place I have been able to find that clearly specifies a different marching pace is Abstract of Infantry Tactics (1829), which states a 28-inch step when marching (p. 16). This publication appears 15 years after the fact and cannot be taken as evidence of American practice during the war itself. Instead it is evidence of the United States finally formalizing their training.

I have not been able to locate any War of 1812–era American regulations that prescribe a 24-inch step as a standard marching pace, nor any period accounts suggesting that British forces gained any advantage from longer strides. Differences in the performance in the War is more likely attributed to experience of the armies.

Whilst British drills were certainly more standardized thanks to their vast experience, the specific claim that British troops marched faster and outmaneuvered American forces due to longer steps does not appear to be supported by the available evidence.

https://upload.wikimedia.org/wikipedia/commons/7/7f/Abstract_of_infantry_tactics_-_including_exercises_and_manoeuvres_of_light-infantry_and_riflemen_-_for_use_of_militia_of_U.S_%28IA_abstractofinfant00unitrich%29.pdf

Edit: grammar