Perhaps not all viruses that jump species barriers are more lethal, but we care most about the lethal ones for sure, and lethality or host damage is a side effect of high replication, so yes I agree with your analysis.

I also said:

I think it is plausible that this happened and HIV causes novel problems in humans, but it certainly has not been well demonstrated, mainly because HIV doesn't cause specific symptoms and it is extremely difficult to properly dissociate other causitive factors.

I'm reading the OBrien Goddert response now that cites some animal studis showing how some animal HIV analogs do fulfill koch's postulate now. I am reading into the sources, but I wasn't aware overall that they had found animal HIV analogs that caused AIDS like symptoms. I'll have to update towards the 'HIV is more pathogenic' stance if this all checks out.