Since you say (in your bounty) that explanations from the books are acceptable, I'll give it a shot. I don't think we've learned enough in the TV show yet to know conclusively if conditions are the same there. There'll still be some conjecture, but based on information from the books.
As you say, over half of Earth's population lives on basic support, or "basic", the government aids you refer to. It's not very lucrative, and it's not exactly a status symbol. In the corresponding scene in the second book Caliban's War, the urban area surrounding the UN complex is very high-end, and she meets only well-to-do people (although we learn some stuff about basic there); a lot of what we know about people on basic, especially on the lower end of living conditions, comes from the novella The Churn:
Burton's misfortune was to be born […] in an age when the division in the popular mind was between living on government-funded basic support of having an actual profession and money of your own.
And just to be clear, although in the books Martian propaganda has made Draper believe otherwise, basic is not a hand-out of money from the government. It's more like receiving goods you need to survive:
Everywhere, all through the city, space was at a premium. Extended families lived in decaying apartments designed for half as many. Men and women who couldn't escape their cramped space spent their days at the screens of their terminals, watching newsfeeds and dramas and pornography and living on the textured protein and enriched rice of basic.
Most characters on basic that we meet in the books are very low class:
Baltimore was Earth writ small, crowded and bored. Its citizens were caught between the dismal life of basic and the barriers of class, race, and opportunity, vicious competition and limited resources, that kept all but the most driven from a profession and actual currency.
These people live in the conditions you mention. They probably don't represent the majority of people on basic, though. The Expanse's Baltimore is mostly a flooded slum.
And many of them resort to crime to earn any comfortable living, or to "escape basic", as they put it. Being on basic is not something to strive after.
She'd escaped basic, she'd had dear friends and mentors when she was working, she'd been able to retire up in the ad hoc structure of the city's underworld. Many, many people hadn't been anywhere near as fortunate as she had been.
It's not clear if "escaping basic" means going completely off the grid. If so, these criminals' lifespans are probably not part of the statistics. Medical care waiting lists are longer for people on basic, so presumably they drag down the average lifespans. We also learn that people who are unregistered births, living off the grid all their lives, do what they can to not get registered and end up on basic. Of course, being unregistered, their lifespans are not part of the statistics.
But this is not the case for everyone. In Caliban's War, basic is mentioned as being adequate for a normal life, although as this is told from Draper's perspective it's not clear how much of this is Martian propaganda to portray Earthers as lazy (she questions this herself). Here, in the Hague, people don't escape basic by resorting to crime, but by working in coffee shops, and they do it in order to apply to higher education:
"Is everyone who works here [the coffee shop] the same age?"
"Well, she said. "Pretty close. Gotta collect your pre-university credits, right?"
[…]
"Okay, so, if you apply to a university, you have to have at least a year of work credits. To make sure you like working. You know, so they don't waste classroom space on people who will just go on basic afterward."
This implies that a good chunk of young people on basic who are not living in bad conditions, choose to take entry-level service jobs in order to go to university.
So, to summarize, over half of Earth's population is living on basic support due to overpopulation and automatization of labor. Of those, many lead perfectly normal lives, such as the teenagers Bobbie meets who take on a year of working to go to university. The ones that live in cities that were hit by global warming (like Baltimore) are basically living in slums, however. All people on basic likely have lower life expectancies than the other half, who work and earn money. Whether an average life expectancy of 120 years (discounting the unregistered people and possibly people who moved from basic to a life of crime) is right or not is hard to say, but Earth's life expectancy being lower than Mars's is almost certainly correct.
