Questions concerning synaptic input and dendritic processing
Started writing a comment and realized it was an answer...

These guys are basically saying "take a uniform spherical neuron" the same way you would say in physics "take a uniform spherical cow." There isn't a dendrite mentioned in the whole paper.

By "the membrane time constant" they mean exactly that: one membrane time constant, effectively the somatic time constant. They aren't talking about dendritic trees: they are essentially saying assume a uniform spherical neuron that gets inputs on its soma.

Membrane time constant is associated with the rate of change of the membrane voltage; synaptic time constant is associated with the rate of change of the synaptic current (this is what they refer to when they talk about exponentially decaying synaptic currents). Real biological synaptic currents have a time course governed my neurotransmitter concentrations and the gating properties of postsynaptic receptors. Real biological postsynaptic potentials (voltages) are governed by both the time course of the synaptic current and the capacitive properties of the membrane (i.e., the membrane time constant).

Instead of considering synaptic time constants, you could simplify a synaptic event as an instantaneous current impulse: essentially the entire current all in one instant rather than over time. The presence of the membrane time constant helps with making this assumption somewhat reasonable, because the membrane time constant ends up filtering input currents anyways, whether they are impulses or have a synaptic time constant. 

In a simulated environment, you can make computations simpler by just adding a little time to the membrane time constant to roughly simulate the effect of the membrane time constant + synaptic time constant. Again, this is for computational efficiency, like when you assume a cow is spherical, not for perfect biological accuracy.