I conclude this thread by saying this:
I finally read the literature. It says that in those cases where we work with linear-elastic, prismatic beam-column element without member loads, a minimun of 3 integration points is required to represent exactly a linear curvature distribution along the element, since the command nonlinearBeamColumn is based on Gauss-Lobatto quadrature rule.
(Lobatto quadrature: http://mathworld.wolfram.com/LobattoQuadrature.html )
My confusion was in the fact that I thought the command nonlinearBeamColumn was based on the Gauss-Radau quadrature rule.
(Radau quadrature: http://mathworld.wolfram.com/RadauQuadrature.html )
In this case, you just need a minimun of 2 integration points to provide the exact solution for linear curvature distribution.
Problem using "element nonlinearBeamColumn ..."
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Additionally I want to add something else... Even if an uniformly-distributed load is applied along the linear-elastic, prismatic beam-column element (through the use of eleLoad -ele $eleTag1 <$eleTag2 ....> -type -beamUniform $Wz <$Wx>), a minimun of 3 integration points will be required too. The loss of accuracy will appear if one applies point loads on the element, as Silvia said, entailing an increment in the number of integration points in which sometimes is necessary to provide up to 10 in order to get better accuracy.