As for BASIC, IIRC it has PEEK and POKE that do direct memory manipulation though not as versatile as pointers. Which language is more high level now?
More importantly, some people take "high level" to mean more powerful and capable of more subtle control of a computer; others take high level to mean more abstracted from the hardware.
By the first definition, C++ is more high level than BASIC, by the second definiton BASIC is more high level (and your average scripting language like python or perl even more so).
So, what do you mean by high level? I still think you and your other correspondent are arguing English semantics.