Apparently when Sondra Perl wrote "The Composing Processes of Unskilled College Writers," the term "basic writer" hadn't yet caught on. Perl, in fact, doesn't seem to like the way Shaughnessy characterizes basic writers. She notes, "These unskilled college writers are not beginners in a tabula rasa sense, and teachers err in assuming they are" (38). Certainly Shaughnessy didn't mean that basic writers had no backgrounds, and Perl thinks that Shaughnessy is right to focus on the logic of basic writers mistakes--but Perl wants to focus on process more than product.
Perl shows that basic writers had just as much logic behind their writing process as Shaughnessy showed that they have behind the written product. They think about the topic, they write, they correct errors, and they do this all rather systematically. So basic writers aren't just going at writing willy-nilly. The question is, what are they doing wrong? Perl seems convinced that it is a preoccupation with error and the attention that it draws away from content that is the problem. This is at least partially confirmed when the process and product of the personal writings are compared to the objective writings--students wrote more fluidly for the personal writing, and although they were still less than perfect, they were better.
It seems that since Perl is particularly concerned with process, she would be in favor of a curriculum like that at my university, where most of the assignments in basic writing are of a personal nature. Although the students may not always have the opportunity to write personal essays, if writing personal essays helps them change their writing process for the better (so that they think more about content and less about errors), that improved process might eventually carry over into more academic writing.
Perl, Sondra. "The Composing Processes of Unskilled College Writers." 1979. Cross-Talk in Comp Theory: A Reader. 2nd ed. Ed. Victor Villanueva. Urbana IL: National Council of Teachers of English, 2003. 17-42.