  The tree-level contributions to the rare decays B+ --> pi+ nu anti-nu, B+ -->
K+ nu anti-nu, and B+ --> K*+ nu anti-nu are analyzed and compared to those
occurring in K+ --> pi+ nu anti-nu, D+ --> pi+ nu anti-nu, and Ds+ --> pi+ nu
anti-nu. It is shown that these purely long-distance contributions, arising
from the exchange of a charged lepton, can be significant in B+ decays for an
intermediate tau, potentially blurring the distinction between the modes used
to extract B --> tau nu and those used to probe the genuine short-distance b
--> (s,d) nu anti-nu FCNC transitions. Numerically, the tree-level
contributions are found to account for 97%, 12% and 14% of the total B+ --> pi+
nu anti-nu, B+ --> K+ nu anti-nu, and B+ --> K*+ nu anti-nu rates,
respectively.
