It wasn't necessarily aimed at Lannister offspring - just Baratheon vs others in general. The Baratheon bastards have a variety of mothers (and Gendry's was blonde, which is possibly a good test case against the Lannisters), which implies that Baratheon features are generally dominant. I don't remember any Baratheon bastards having Lannister mothers, so we never actually get a concrete test of the dominance between the two houses. Anyway, based on the little info we have, the whole premise of judging people according to appearance is a bit shaky. It is interesting though how often the features in the major Houses tend to breed true - Stark, Tully, Baratheon, Lannister, Targaryen all have distinctive colouring. To be fair though, the Targs are crazy inbreds, so that would help.
Nitpicking, but there may be others who know. I mean, you're right - Howland Reed was the only other person there - but there is the chance that either he or Ned told other people about it. Benjen, for example, or the Reed children. Considering Ned didn't even tell Catelyn though, it seems unlikely that he would have told anyone else (and maybe that's part of what his promise to Lyanna entailed).