In this scenario person B ("if they made it to adulthood then they could easily live to 70") is more right, but still only providing part of the answer. Like most things in life, the truth is far more complex, and fun, than broad strokes can encapsulate.

To start, demographers are statisticians that study human populations. We combine information from raw numbers, like births and deaths and migration, to arrive at fun measurements like age-specific fertility (number of live births per 1,000 women of a certain age) and, of interest to you, life expectancy. We then compare those numbers across populations and across time to try to gain insight into the changing human experience.

If the data is good we are able to tease out the specifics of life expectancy by combining all that raw data on deaths to construct a life table. That life table will enable us to say for this specific population at this specific time the average 19 year-old in the U.S. (for example) can expect to live for roughly another 60 years. If you want to play around with a calculator instead of looking it up on a table check out the U.S. Social Security calculator.

As you can see, your life expectancy very much depends on how many years you've already lived. Before major improvements in sanitation and medicine a higher infant mortality rate would, on average, bring the gross average life expectancy down. If you looked at life expectancy at 5 years old (the typical break point demographers use to avoid the influence of childhood mortality), you would see a jump in expected average life expectancy. Wikipedia has a nifty table to explore the life expectancy of different populations over time. You can see in that table they specifically mention certain break points, like 5 years or 10 years, after which an individual can expect to live for much longer than the overall average. In the scenario you posted, person B is more right, but there is still a lot of fun to be had diving into why they were more right.

Finally, a word of warning. Even with all the best data available in the U.S. we still make mistakes when compiling demographic information. Determining life expectancy from skeletal samples, and even fairly complete church documents detailing births, baptisms, and burials, is a complex business. As a discipline we are getting better, but remember that any number used for life expectancy is a guess, an educated guess, but nonetheless a guess.

To add to/simplify greatly on /u/anthropology_nerd, a good rule of thumb is that people could certainly live long lives, but at every stage of life death was more likely. Old people were still old--nobody thought of forty or fifty year olds as wise elders--but there were fewer of them.

They can both be true. Life expectancy at birth is a single number that doesn't tell you the distribution of ages, or that all 50 year olds are expected to die any day, which is the point of the second group.

You don't have to go back to the tenth century for these numbers either. As recently as 1900, the life expectancy at birth was under 50, yet there were still plenty of old people. We just lost 16% of babies which really pulls down the average. There are reports that over half were lost if there were food shortages.