I believe the thinking now is that terrific horses than can get a distance have larger than average hearts, and that, it's believed, is a genetic trait that is carried on the X chromosome, so male horses can only inherit the larger heart via their mothers. Ergo looking to the dam's side, rather than the sire's for distance indications.
Of course, lots of things go into whether a horse can run a distance, but a large heart is a good advantage to have, and it can only be passed via the X chromosome.
I remember reading somewhere that in female horses, both X chromosomes must carry the gene for the larger heart for the filly to be born with one, so while Lady's Secret likely received the gene from her dad, her mother must also have carried it.
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