Some of both, but I think the second effect is dominant. The rest of this post is all my analysis from scratch as a non-EE, so hopefully it makes sense.
Let's say we have an antenna at the end of a 100-meter (electrical length) lossless transmission line that's mismatched to the antenna by a 10:1 SWR. We'll assume that there's perfect reflection at the transmitter end of the feedline (so the transmitter is a perfect current source, doesn't dissipate anything, and can withstand whatever voltage is necessary).
10:1 VSWR is an 0.82 voltage reflection coefficient, which amounts to a 0.67 power reflection coefficient. If we send a pulse from the transmitter, 33% of power goes into the antenna and 67% of power gets reflected down the feedline, reflected again, and comes back for another try, 33% of that 67% is absorbed by the antenna, etc. etc. Those two trips along the feedline take 667 nanoseconds. $ 0.67^2 \approx 0.45 $, so after 1.5 round trips, over half of the power has made it into the antenna. Those 1.5 round trips take 1 microsecond, so any modulating signal with a bandwidth less than 1MHz will survive pretty much intact. $ 0.67^{12} < 0.01 $, so after 11.5 round-trips, more than 99% of the power has been delivered, and anything under 130kHz is going to have pretty much undetectable distortion. Since our signals on HF are almost always under 6kHz wide (and usually under 3kHz) this seems pretty safe.
Modifying our simplified system by adding loss in any part of it, or making the mismatched section shorter than 100m, or making the SWR lower than 10:1, all make the reflections die down that much faster, giving a more favorable result.