I (and several of my colleagues) noticed this when we first got our BRNAV fit. I recall chatting about it but never reaching a firm conclusion.
To summarise so far; there are several possibilities.
1. Its a figment of our imagination. An apparerent effect we notice, whilst mentally disregarding countary evidence. To reach a conclusion about this would require a rigorous experiment; as in data gathered in controlled circumstances.
2. Its an indication thing. Something to do with how the nav system performs its calculations. Something like Bulletheads suggestion, maybe related to generally getting less drift when you have a tailwind. Could it be as simple as someone wrote an algorithm for doing the calculation, and just simply got it wrong, and <insert your avionic manufacturer here> has been using it as a library routine ever since? I know it sounds unlikely, but .... wierder stuff has happened in IT before!
If its not one of those 2, then its a real effect, in which case:
3. Something to do with the air mass you're flying through such that a tailwind generally means your true altitude is decreasing, the pay off being an increase in IAS. As per Cows.
4. How about something to do with Earth Curvature? There is a very small performance increasing effect caused by this; in Level flight lift is actually slightly less than weight because the aircraft is not actually in a 'balanced forces' situation because its not actually following a stright line. However the effect is pretty minimal at aircraft speeds. However it does exist, so the faster your groundspeed the less lift you need, which would translate to less induced drag and a higher IAS. However, without doing the calculations, I would be gobsmacked if it could account for more than a fraction of a knot.
4 is a real effect, but just not big enough. 3 needs more investigation.
pb