If Briggs used different piston ring groove dimensions with the chromed rings, it sounds as if they specifically didn't want people to fit them interchangeably with the plain cast iron rings. This may perhaps have been because they wanted to be fairly sure nobody would fit chromed rings, or steel rail oil rings, to an engine with an aluminium bore. I've certainly never been prepared to do so myself.
Looking through the
factory parts list, it seems that there was a change in piston design, during this model's production run.
Both 'Standard' and 'Standard, Chrome' ring sets were available for the earlier type, used 'Before Code Date 01060700'.
But the Chrome ring set wasn't offered for the later piston, used after that date.
So it would appear that the supplier is correct in this case,
if they are supplying the late type piston.
If the original piston was re-used, chrome rings could be used too.
The chrome ring sets Briggs supplied were somewhat a 'field expedient' really. Used to get a bit more use, without excessive oil consumption, from a tired engine that wasn't worth the cost of reboring/honing out and oversize parts. They do work in the aluminium bore engines too, and were available for most of them.
But with labour costs these days, these rings wouldn't be in much demand, in the US at least. Not much more money to fit a new engine over there, compared to an overhaul.
From the Briggs #270962 Repair Manual:
NOTE: Chrome ring sets are available for some engine models. See Service Bulletin #479 or Illustrated Parts List.
Chrome rings are used to control oil consumption in bores worn up to .005� (.13 mm) over standard. The
cylinder bore receiving chrome rings does not need glaze breaking or cross hatch.