Is this true or just a trick used by hardware salesmen?
It's bollocks. If you take a strike on a network cable, it'll go right through the card and into the PCI bus, which will make your system just as dead as if you'd had the NIC built-in.
The chances of getting a dangerous power surge on a network cable are very low, but if such a surge did happen and was only moderately dangerous then a separate NIC may afford you a little protection (it might pop a chip or other component on the NIC and but not affect the motherboard, were-as on the motherboard most of your I/O tech is controlled from one chip so if it pops everything could go).
The only even slightly likely way you could see a significant surge on the line is something drastic like a lightning strike though, and in this case any arc that affects the NIC is going to be able to jump across to other nearby machine parts too (or may at least fry the PCI bus that the card is plugged into). So the minimal difference a separate NIC will make is so small in the scheme of things as to not be worth considering. Small surges (perhaps caused by malfunctioning equipment at the other end of the line, or just normal day-to-day random conditions) network adaptors are designed to cope with anyway.
A network cable doesn't deliver power; only ports are powered (NIC, switch, hub).
The benefit to having a NIC separate from the motherboard/etc is that if the NIC fails (RealTEK chipsets used to be particularly notorious), only the NIC is toast. If the NIC is onboard (incorporated into the motherboard), you lose the NIC and possibly other functionality due to circuitry.
An electrical surge normally occurs on the power line, not the network cable. As such, it makes no difference whether you use a built-in or add-on NIC.
I've never heard the electrical isolation argument and frankly I share the view in the other answers, the scenarios where it might be true are going to be vanishingly rare. Additional NICs are a good idea for redundancy and additional bandwidth reasons though.
I'm not concerned
Power lines are a more likely surge vector, except for ESD.
The thin wires that modern networks use have a high impedance and a noticable amount of actual resistance.
Furthermore, these wires are almost always used entirely indoors. So, it's hard to imagine a scenario where a really destructive spike could be generated, except for the case of ordinary ESD -- electrostatic discharge.
If a NIC was damaged by a very low current but high voltage event like ESD, then I would not expect it to propagate through the system, and yes, a replacement NIC would help you in this one scenario. This kind of surge doesn't typically have secondary arcs but does have enough energy to damage the microscopic circuits inside the first IC that it hits.
But the network devices have circuits that are supposed to protect the IC from ESD events, so these would have to also be overloaded for any damage to occur.
Overall, I think it's just a theoretical argument. We don't see ethernet transceivers failing often. Other misfortunes are far more likely to appear, so I wouldn't arrange a system around this concern.
If you're really concerned about power surges passing into your systems, which I have seen, especially in multi-level installs, replace the copper with fiber. We're ranch style now, but in our previous building we had multiple floors and ran fiber between floors instead of copper.