62/63 are, indeed, currently designed by BA as exit rows in the system. So until BA revises this designation (which may not be until the CAA revises its definition), the Res staff's position is correct.
[KVS Availability Tool 3.3.1/Platinum - Amadeus Seat Map: 01 Dec 2008/BA 117/LHR-JFK/744/C]
Code:
A B | D E F G | J K
12 + -
13 - + + + + + - -
14 + + + - + + - +
17 + + + + + + + +
18 + + + + + + + -
19 W + + + + + + + +
20 W + + + - + + + +
60 U - + + -
61 U - + + +
62 U - - + + E
63 U + + - + E
64 U - + + +
[+] Available [-] Unavailable [W] Wing [E] Exit Row