Not sure if it's just miscommunication, or you misunderstand how HAART works, because you said "That is literally exactly what I said", and then in your next sentence repeat the statement that is false, "becoming more resistant to one means becoming more susceptible to another."
For example, suppose you take ATripla, which is a combination of efavirenz, emtricitabine, and tenofovir. If a viral particle has a random mutation that confers resistance to, say, efavirenz, that mutation does not make the virus more susceptible to emtricabine or tenofovir. The fact is the virus was already susceptible to those two drugs (that's why you take tests that specify your viral strain's pre-existing resistances to determine the best drugs for you before you start HAART), so it still is unable to replicate.
It's just a matter of statistics, not that resistance-granting mutations naturally make the virus more susceptible to other drugs.