Moving further means increased commuting cost. For drivers this comes in the form of massively increased fuel costs. For transit users this comes in the form of increased fares, since BART practices distance-based pricing.
Commuting daily from Fremont to SF costs $12, that's over 1h of minimum wage. Imagine if you had to pay 10-15% of your total income (pre-tax!) just to get to work. More if you're unable to get a full 8h of work a day.
Moving further also means a large reduction in disposal free time. Free time is a bit of a misnomer when it comes to the poor though - since the time isn't actually free. The article touches on this at a few points - the working poor require a lot of government subsidies and aid organizations for survival, all of which takes time, and most of which are located in SF.
One of the key inhibitors in helping people out of homelessness is, to be simplistic, lining up for things. The basic services they need to survive have huge lines to access them, making a large proportion of their lives idling in a waiting room, waiting for one necessary thing after another. Imagine the DMV, but every day, and multiple times a day.
All of this exacerbated by living far away. Not only are you waiting around forever for basic things, you're now spending more time to get there in the first place.
Even to a rational, completely-informed actor (an unsafe assumption, to say the least), the economics of living further away may not actually work.