Reading this, I think there may be some confusion as to the double-meaning of "leaky."
Mr. Carlson's tester is for parallel resistance which will "leak" DC current. (That is, an ideal capacitor, wired in series, will block DC current—once it is charged, no DC current will flow.)
Electrolytic capacitors have an electrolyte that is a liquid or goo and they sometimes leak that material out, visually indicating the capacitor is no good.