CFI logging instrument time

A CFI with airplane single-engine rating but not instrument-airplane (not a
CFII) gives flight instruction to a private pilot. Part of the flight is in
the clouds, with the private pilot flying. Can the CFI log instrument time
under FAR 61.51(g)(2):

"An authorized instructor may log instrument time when conducting instrument
flight instruction in actual instrument flight conditions." ?

One can argue that a CFI without the CFII is not authorized to give
instrument flight instruction, and therefore can't log it. This leads to a
related question: Is this CFI exceeding his privileges (61.193, see also
61.1(b)(10) ) by providing such instruction (in or our of the clouds), such
as additional training to a pilot working on an instrument rating?

Please cite a reference if possible. I couldn't find this in the Part 61
FAQ (http://www1.faa.gov/avr/afs/afs800/docs/pt61FAQ.doc).

Barry