it matters more if the lineage is only 1 degree of separation (like for ajlongspiano) for how long they studied w/ said person. so for me, knowing my current teacher-performing artist plays incredibly! teaches so well (and reviews/remarks by current and former students validated this in search-instructor selection process)- regularly concertizes, records/releases CD's (that receive very good acclaim) and participates in int'l festivals, than the fact they studied with a certain someone for over many years (and that this someone was their most recent instructor), I get the benefit of my teacher's style, talent, experience first, but my teacher can also draw on instilled philosophy, tricks/techniques, direct experience, etc from their study with a certain (very famous'-and for good reason) someone for so many years. Also, that I like my teacher's style (delivery, methods, personality etc). that is important to. You should feel like at the end of a lesson like it flew by, not 'drag on', if you find yourself asking what time is it/when is this over? during lesson, things my no be optimal.
I for one feel very fortunate and a sense of responsibility to apply/learn as well as possible given my opportunity that so many others (many way way more talented than me) would love to have. It pushes me to work harder during the lesson and do my best to bring an appreciable amount of application and progress on assigned tasks to next encounter.
so like most things it depends.
However someone that was a student that was a student that was a student of d'Albert, or did a semester with a student of Reinecke 30 years ago late int their training, etc., that probably has less impact due to degrees of separation, total exposure (and how formative was the experience for them), and how long ago said study likely occurred? , that wouldn't matter much to me in the least.