Apart from wondering both how researchers know that HEks don't spend so much time on computers, and why they assume that spending time using them is so terrible, I'd say this piece from the Guardian has got it about right. The Guardian is getting its story from a Review of Primary Education, but the research on home education that in turn informed the review is questionable in some regards.
From the review:
"In the midst of the many differences in philosophy, outlook and practice of home schoolers, from those who follow the national curriculum pretty rigidly to those whose approach makes Summerhill seem like a model of mainstream pedagogical rectitude, home schooling appears to consistently offer children a more efficacious educational experience even as measured by the standards of normative performativity. One constant in the midst of much complexity is the better than average performance of home schooled children when compared to age cohorts in the general population. Rudner's (1999) study illustrated that those in grades 1-4 who are educated at home, on average, perform one grade level higher than their public and private school counterparts. Lest this be thought as an effect of early nurture likely to dissipate later in the child's educational development, it is striking that the performance gap expands as the student progresses so that by 8th grade such children are performing at four grades above the national average in the US."
Actually, I think they may have that last bit completely right. Over and over, we see HEks starting apparently slowly, (ie: gathering information in a much more ad hoc sort of a way, according to interest and real life experience) then going on to perform very strongly by the usual academic standards.
Ho hum. We can only hope that this message finally gets through to any priggishly pedagogic LA inspectors.
There are more takes on the story from The BBC, The Independent and The Telegraph.
Update: Ah, a possible explanation for the minimal computer use assertion has emerged, (thanks Fiona N). It seem quite possible HEks have been conflated with Steiner pupils, the latter group being heavily discouraged from computer use. Most HEks aren't kept in the dark ages.
Further update: Ok, Fiona N now tells me that the assertion that HEks use computers less than schooled kids comes from outdated research on largely religious US homeschoolers. It certainly doesn't match our experience here.