LARGE (IIRC, > 4" diameter) healthy trees on a dam should be left alone, as live roots are less likely to cause leaks than dead, decaying roots. I tend to agree with the PMs who feel that trees on dams may need careful trimming to reduce their "sail area" and hence their chance of being blown over in strong winds.
When removing large sick or dead trees from a dam, I think an extensive dam rebuild (carefully excavating the roots, repacking with good clay, perhaps after lowering the water level) is in order.