Hi Glenn,
More information would be needed to determine the relationship between Bill and Mary. The fact that a testing company or 3rd party matching site has indicated that each may be a 4th cousin to your wife, doesn't necessarily mean that they are related to each other. To start with, you would want to find out if Bill and Mary are actually DNA matches for each other, and if so, the amount of shared DNA between them. Then you/they would need to research and build out each of their trees to find the MRCAs for each relationship to your wife and to each other, based on the shared DNA among each pair of matches.
Even if research determines that Bill and Mary each turn out to be a 4th cousin of your wife, that research may show that each is related to your wife through a different line. If so, they may be unrelated to each other (at least in recent genealogical time frame terms). Conversely, if that research shows that they are both 4th cousins to your wife related through the same line, they could be biological siblings (though, not likely). It's also possible that Bill and Mary could be related to each other through a shared ancestral line that your wife doesn't share with either of them.
Also, if an endogamous population is involved, it's not uncommon for a married couple to be related to each other through one or more of their ancestral lines.
