That sounds to me like the dealer trying to upsell additional products. HDMI is a digital cable and its behavior has nothing to do with the behavior/type of any analog related cables (such as interconnect and power cable). I have evolved as someone who does not like silver in their system (for power cable, fuse, interconnect, speaker wire). However, I recently discovered that this does not include digital type cable and silver/silver-plated digital cable actually works much better than normal copper. It has to do with how fast the HDMI conductor will charge and discharge the voltage. Since we are talking about square waveforms here (as a form of digital communication), the silver wire will have an added benefit to the digital RF square waveforms.
However, when using silver in an element that has a direct contribution to analog circuits (power cord, outlet, fuses, speaker wire, interconnect), silver behaves in a completely different way and definitely affects the sound here. Silver in an analog circuit is like putting in an op amp that has a very fast slew rate. What happens is that waveforms tend to get translated into a higher frequency than what they are supposed to be. (hence the tendency to push upper mids/highs and to be lean on bass)
In your case, Wire World Platinum use solid silver conductors. The Silver Starlight use silver-clad OFC copper conductors. I don’t have any experience with this directly because I haven’t purchased a cable as expensive as the Platinum, but the Platinum solid-core silver may have an edge over the Silver. The silver-clad copper may have some slight capacitance in the copper inner core that could affect how fast it charges/discharges. This could affect things like jitter and square waveform bit accuracy, but once again someone would really have to test these two cables to see if they can hear any difference. At this level, you’ll have to have extremely high resolution equipment and cables to really hear that difference. (i.e. $$$$)
