Looking at the logs from my Michigan spiders page there are a lot of hits on the Brown Recluse pages. I thought I'd clip and summarize a few of the better resources on the net on that topic, with a specific eye toward that spider's presence in Michigan.
Before I do anything remember that some spider bites can be life threatening, and that some wounds from other conditions mimic spider bite wounds. If bitten, remain calm and seek medical attention.
First, as to whether the spider is common to Michigan or not - let's look at some maps. From Brown Recluse Spider by Michael F. Potter, urban entomologist from the University of Kentucky:
Distribution of the brown recluse spider (dark shading) and other species of Loxosceles spiders in the U.S. (light shading) (adapted from distribution map of R. Vetter, Univ. Calif. Riverside) As you can see, the nearest distribution is mid-Indiana and southern Ohio.
Second, as to whether a particular bite is from a brown recluse or not, and the diagnosis of the wounds you get (nasty necrotic sores), the Potter article has this to say:
Spider bites are difficult to diagnose, even by physicians. Contrary to popular belief, it is exceedingly hard to diagnosis a brown recluse spider bite from the wound alone. Many medical conditions mimic the necrotic-looking sore from a recluse bite, including bacterial and fungal infections, gangrene, and diabetic or pressure ulcers. Several recent misdiagnoses have arisen from outbreaks of drug-resistant infections by Staphyloccus aureus. The bacterium produces painful skin lesions that resemble recluse bites, and can run rampant in close living quarters such as hospitals, nursing homes, summer camps, military barracks, and correctional facilities. Similar-looking lesions can also be caused by other types of insects and arthropods.
I'll spare you the pictures, though you should go look if you need to. Vetter has an article Causes of Necrotic Wounds other than Brown Recluse Spider Bites (2004, UC Riverside) in which he concludes that medical personnel vastly overdiagnose brown recluse spider bites even in places where those spiders are never found:
Throughout the United States, spiders get blamed as the cause of many dermatological wounds in medical diagnoses. In virtually every case, NO spider is seen nor felt inflicting a bite, nor is the alleged spider collected in the incident. “Potential spider bite” diagnoses are made solely on the symptoms of the lesion. In the case of necrotic wounds, “brown recluse spider bite” is a very common conclusion of medical personnel throughout North America including such ludicrously inhospitable places as Canada and Alaska where no brown recluses have ever been found. This is in spite of the fact that the brown recluse spider (Loxosceles reclusa) is native only to the South and central midwestern states (circumscribed by southeastern Nebraska south to Texas, east to Georgia/westernmost tip of South Carolina and southernmost Ohio with additional rare finds being made beyond this area).
The American Medical News from the AMA in 2002 has a story Convenient culprit: Myths surround the brown recluse spider
The reputation of the shy, retiring Loxosceles reclusa far exceeds the spider's range, confusing efforts to diagnose or accurately track the true incidence of its bite.
In short: it probably wasn't a brown recluse that's responsible for that spider bite in Michigan.