Let's look at an H-R diagram:
Image courtesy of Wikipedia user Saibo under the Creative Commons Attribution-Share Alike 2.5 Generic license.
Were we to draw a (vertical) line across the diagram corresponding to spectral class F8, and a second (horizontal) line corresponding to an absolute magnitude between 12 and 13, we would find that the two lines cross in an area of the H-R diagram populated solely by white dwarfs, near the bottom left corner.
Main sequence F-type dwarfs are much brighter - brighter than the Sun, often by an order of magnitude - while main sequence dwarfs with absolute magnitudes comparable to the stars in this binary system are extreme M-type red dwarfs.
All this you know. There is more evidence that suggests that these are white dwarfs.
White dwarf masses are typically between 0.3 M$_\odot$ and 1.39 M$_\odot$, with the latter being the Chandrasekhar limit - the maximum mass a white dwarf can have (see Kilic et al. (2007) and Kepler et al. (2007)). However, most white dwarfs do not reside at these ends, but closer to the middle.
If the mass of the second star is greater than the Chandrasekhar limit, then it cannot be a white dwarf.1 However, if the minute deviation is due to some measurement error - a possibility - then it could still be a white dwarf, albeit a very massive one.
Red dwarfs, however - the only other possibility, if the absolute magnitude is correct - never get anywhere near 1.4 M$_\odot$, or even half that limit. Therefore, it seems highly unlikely that the second star is a red dwarf. Perhaps the first one is, but the second one is not a main sequence dwarf. A white dwarf is the best explanation.
In short, other stars with this spectral type are way too massive and too luminous, and other stars with this absolute magnitude are not massive enough (for one of the stars).
I'm not sure what the V is doing in the classification. Assuming we're using the Yerkes system, this would indicate that it is a main sequence star, as you said (white dwarfs are denoted with a 'D'), so this leads me to think that perhaps some variant or non-traditional system is being used.
Second potential solution
It occurs to me that these stars could be subdwarfs, less massive than their counterparts of the same spectral type. They're hotter and fainter than most subdwarfs I'm aware of, but perhaps this is an exception to the rule.
Subdwarfs lie below and to the left of Sun-like stars on the main sequence - closer to them than white dwarfs, but still appearing a bit like both groups. They have the designation 'sd' in the Yerkes system, which again does not agree with your information.
1 There may be exceptions. See SN 2003fg.