I'm ready to eat crow with regards to claiming many other agencies teach mod's based on 1.6 ppO2. The only recreational agency I can verify is IANTD. Looking back on my first post, with much embarressment, it was badly worded except for the last sentence.
If given a second chance, I'd start with the NOAA nitrox tables. After a couple hours e-research, it seems most recreational nitrox tables are versions of these. Apendix F of my IANTD Nitrox Manual reprints NOAA Nitrox II (36%) documents, containing this pertinant sentence. "The normal depth limit for this mixture shall be 110 feet/30.3 M of seawater for dives that do not require decompression".
My image of NOAA diving is that it's not recreational, not hard hat either, but the divers are working divers. IANTD was the first to bring nitrox to recreational diving and maintaining the same tables for non-working divers gives a cushion of additional saftey to recreational divers.
PADI's (and others) use of the NOAA nitrox tables is more conservative in that it relegates the 1.5 and 1.6 ppO2 columns to contingency or emergency. There very well may be wording somewhere similar to Forays and I hope there are instructors that might use similar terms.
My TDI Nitrox; User Friendly Guide to Eanx, page 26, bottom paragraph, states: Maximum scuba diving limit for the partial pressure of oxygen should not exceed 1.6 ATA and should not have a bottom time longer than 45 minutes. Use 1.5 ppO2 (or less) for bottom times between 45 and 120 minutes. A ppO2 of 1.4 (or less) is recomended for particularly strenuous or cold dives (sic). I'd like to assume that 's how TDI/SDI teach recreational nitrox diving.
ANDI was second in the recreational use of nitrox and may also not darken the 1.5 and 1.6 columns of their NOAA based nitrox charts, but I do not have one of their manuals for verification, and I do not know of any ANDI instructors or shops.
As I see it, if you are healthy and in shape enough that recreational diving is not strenuous, cold water diving would be the reason to limit ppO2 to 1.4, although current at depth would cause me to adjust mod accordingly. If you only dive strenuous or cold dives a 1.4 agency is fine. 1.6 might allow you to peak under the house of the USCGC Bibb (Key Largo) without paying more for a custom blend.