That's a fairly brief characterization, and I'm working on cleaning it up a bit; there are problems with Searle's original formulation--mostly due to confused terminology and an unwillingness to accept certain things (like emergentism)--but I think he's basically got the right idea. Still, this isn't a position that's widely accepted in the philosophical community--most people still cling to one form of Functionalism or another.
There is, however, mounting evidence that Biological Naturalism (or something very like it) is starting to catch on in the scientific community. Today's issue of Nature contains a fascinating article about the difficulty of linking specific genotypes--that is, specific genes or specific kinds of damage to specific genes--to individual mental orders (e.g. schizophrenia or autism). The authors suggest that this might be because many psychiatric disorders might be cluster phenomena--in other words, constellations of related disorders that have radically different causes but share similar effects. A gene that sometimes seems to increase the risk factor for schizophrenia might be subtly altering some aspect of brain structure, and this alteration might in turn predispose one toward a certain behavior that might, in combination with another genetic accident, lead to psychosis; the system, in short, must be considered holistically in order to say anything meaningful about higher level features (such as thought disorders).
Vaughn over at Mind Hacks puts the issue even more explicitly in biological naturalist terms:
I couldn't have said it better myself. Mental illness, like conscious states in general, seems to me to me to be an emergent phenomenon: it can't be reduced to any one gene, neuronal process, or even type of brain activity, because the same phenomenal state can, given variations in the environment (in my broad sense, 'environment' includes neurobiological facts about the subject), be produced by very different physical phenomena. That's precisely why I think intentional (in the technical sense) language can't be eliminated from our "mental" vocabulary--statements about beliefs, desires, hopes, thoughts, and ideas are not reducible to statements about neurobiology, neither in a token/token sense nor in a type/type sense.
Genetics is a complex business, but psychiatric genetics even more so, because it attempts to find links between two completely different levels of description.
Genes are defined on the neurobiological level, while psychiatric diagnoses are defined on the phenomenological level - in other words, verbal descriptions of behaviour, or verbal descriptions of what it is like to have certain mental states.
There is no guarantee, and in many people's opinion, probably no likelihood, that these 'what it is like' descriptions actually clearly demarcate distinct processes at the biological level.