"It's fairly obvious the mother's name was not on the deed, if two people received half the proceeds each"

At the time of sale, sure. People try this tactic to avoid the lookback for Medicaid. You need the other info to establish how basis comes into play.

Everyone overlooks the tax ramifications when they want to maximize the legal ramifications. Or, they overlook the legal ramifications when they want to maximize the tax ramifications.

And typically, they lose on both issues.