Lux and Sornette have demonstrated that the tails of the unconditional distributions of price differences and of returns associated with the model of rational bubbles of Blanchard and Watson follow power laws (i.e. exhibit hyperbolic decline), with an asymptotic tail exponent μ<1 over an extended range. Although power-law tails are a pervasive feature of empirical data, the numerical value μ<1 is in disagreement with the usual empirical estimates μ3. Among the four hypotheses underlying the Blanchard and Watson rational bubbles model (rationality of the agents, no-arbitrage condition, multiplicative dynamics and bubble independence across assets), we prove that the same result μ<1 holds when relaxing the last hypothesis, i.e. by allowing coupling between different bubbles on several assets. Therefore, nonlinear extensions of the bubble dynamics or partial relaxation of the rational pricing principle are necessary