The trade system, when looking at someone else's collection for cards to trade, will sometimes accept a poor match too greedily before looking to see if there's a

As an example, I am looking for 5 Liliana of the Dark Realms: 3 from M13 and 2 from M14. If I go to solkanar44's page, it suggests trading mine for his. He has 2 LotDR from M14 for trade. However, the matcher matches with my M13 wish, so it says that it's a poor match and this match disappears if I go to strict matching, even though I want the M14 version as well.

This sounds normal to me. Can you take screenshots of what you are seeing? Relaxed matching is weird in that it will match both wants showing you multiple lines even if the person only has one version of the card. Since this person has 2 versions of the card you want and you have 2 different wants you may see it listed as many as 4 times on your 'relaxed matching' page. (One will match and be a perfect match, one will match wrong, then the same for the other version). The strict matching though only shows the lines that specifically match the details you requested.

Oh, you appear to be right. I feel stupid now.