I´m not a curator so I can´t do much to solve this problem. But it´s an interesting one and probably often occurrs in other taxonomical groups. In fact there are two separate problems calling for the establishing of a complex in this and other cases: The first one is the fact that not all observations show the necessary diacritical features to distinguish "microspecies" inside some complex (with quite a few observations you´re lucky if you can place them inside some wider group like a family...). The second is that there may be individuals or populations which fit inside a complex but not readily inside some microspecies. In the case of P. aviculare s. lat. J.AKEROYD writes ("Docks and Knotweeds of Britain and Ireland", p. 106f. says "However a reappraisal of Polygonum arenastrum would certainly go much of the way of solving the problem of the small but persistent proportion of specimens that is difficult to accommodate within either P. arenastrum or P. aviculare." That being said the example you give is in my opinion clearly P. aviculare (it looks that way late in the season when most stem leaves are shed and only those on the branches remain).