You are correct in essence - a current over 15 A will trip a single pole breaker eventually, depending on the design spec of the breaker and the ambient temperature (if it's a thermal-magnetic type). Your friend is correct only in that a continuous current of 13.5 A MAY trip the breaker depending on it's design and rating. If the duplex outlet is protected by two independent circuit breakers, each rated at 15 A and operating at 90% of nominal capacity, each will carry a load of 13.5 A continuously (hours? centuries?) before tripping. However, most duplex outlets are on the same circuit protection device (breaker) and the total allowable maximum current draw is the trip level of the breaker - 15A (or 13.5 or 12 or...) which is primarily a function of temperature and is always (or most of the time..) below the maximum continuous current carrying capacity (ampacity) of the downstream wiring connected to it.
Many breakers (US UL-489 type) are rated at 50 C ambient and often run hotter in an enclosure and, as a result, will trip at 80-90% of their rated current (a 15 A breaker at 90% of capacity would trip at 13.5 A continuous current).
Home breakers have two trip modes:
One is thermal and protects against continuous overcurrent, such as the rated current plus some allowance factor which depends on temperature. Typical US ratings are 2-5% allowance factors at 30C, so a 15A breaker will carry 15.75A indefinetly at 30 C if it's allowance factor is 5%. This is thermal, as heating of the breaker's components determines the trip point. However, as I said above, breakers typically run hotter than 30 C (and are actually rated at 50 C if they are UL 489 types), so a 'cold' breaker may carry more current that a 'hot' breaker - thermal element working here.
The other trip mode is surge overcurrent, that is, a current several times in excess of the rating. This has a time component, too, so most breakers will carry 8 x rated current for 8-10 ms (a bit more than 1/2 cycle) then trip. If you put 2-3 x rated current thru them, they will hold for maybe 10-20 cycles, depending on the temperature and breaker design. This is the 'magnieic' part, as it's initiated by the magnetic field produced by the high current.
If you put an outrageous overcurrent thru the breaker, say 40,000 times rated, it may not clear - it can't interrupt the arc that forms when the contacts open. This is the 'interruption' rating of the breaker, which is often stamped on the case somewhere. Typical home application breakers have an interruption rating of 20kA, which is plenty given that the system is fed from a 240 V center tapped transformer with an impedance rating of ~10% - this detemines how much current the transformer can source into a fault.
I'm sure this throws much darkness on the subject,
Be careful. You said: Typical home application breakers have an interruption rating of 20kA... They are actually almost always rated 10kA (10,000A). I think some of your other data is close but not right on, such as the carrying capacity of breakers and how long they are permitted to carry a particular percentage overload before they must trip, in order to receive an Underwriters' Laboratories (U/L) label.
Best bet--go to the U/L standards.
The National Electrical Code in the USA has said for a long time: "110.3(B) Installation and Use. Listed or labeled equipment shall be installed and used in accordance with any instructions included in the listing or labeling." Therefore, the final word in answer to the posted question is that any instructions or directions in the catalog or supplied by the manufacturer, in addition to the limits and requirements of the testing standard and listing by the independent testing authority, shall determine if one or two heaters can be installed.
Of course, the practical answer is always: "Is it safe, does it create an apparent or real hazard?" I would want to see the use of a commercial or industrial grade receptacle, instead of a typical "cheap" residential one, because it has better contact surfaces, better spring tension on the contacts, lower contact resistance, stronger molded plastic parts, and a much greater reliability for the use mentioned in the original post.
Also, the electrical code allows a 15-amp receptacle to be used on either a 15-amp or a 20-amp circuit {see NEC Table 210.21(B)(3)}, and cord-and-plug-connected equipment canot exceed 80% of the branch circuit rating {see NEC 210.23(1)}. Therefore, a 15-amp branch circuit cannot supply a 13.5-amp heater; not even one, let alone two. However, a 20-amp branch circuit can supply one, and if the receptacle in question were supplied from two separate 20-amp branch circuits (along with one's breaking off the metal tabs that electrically connect the two halves of the duplex receptacle together), then that one duplex receptacle could supply two 13.5-amp heaters.