Based on data published by the OECD, the claim that the United States spend more public money on health resources than other developed countries is true. The figures given there for the 35 OECD member states and a selection of additional countries report expenditures on
health care goods and services (i.e. current health expenditure) including personal health care (curative care, rehabilitative care, long-term care, ancillary services and medical goods) and collective services (prevention and public health services as well as health administration), but excluding spending on investments.
In 2013, the year that the video was apparently published, the USA spent 4207 USD per capita on health. This was the sixth highest spending in a list of 44 countries. Luxembourg and Norway had much highest spendings (with 5594 USD and 5084 USD, respectively), while spending in Switzerland, the Netherlands, and Sweden are reported only somewhat higher governmental spendings than the USA (4360 USD, 4300 USD, and 4228 USD, respectively). The United Kingdom, the country apparently referred to by Green, runs at position 15, with 3057 USD per capita.
The same pattern is visible for the years leading up to 2013: Each year, Luxembourg and Norway are two countries with exceptionally high public spendings per capita. The United States is among handful of countries that vying for the ranks immediately below these two exceptions. This pattern supports the claim made in the video that public spending in the USA on health resources was higher than in most developed countries at the time the video was produced.
The pattern changes after 2013: Now, public spending on health expenditures in the USA clearly surpasses that of any other country, including Luxembourg and Norway. This increase in public spending in the USA that sets in in 2014 offsets a notable drop in voluntary spending. I suspect that this is the effect of the Affordable Care Act which came into force that year.
The latest available figure for the USA is from 2016. In that year, the USA is listed as the country with highest spendings per capita with 8047 USD. The amount for Luxembourg, the country with the second highest spendings, was 5643 USD, with Norway, Switzerland, and Germany following (5257 USD, 4912 USD, and 4612 USD, respectively).
To summarize, since 2007, the USA were always among the countries with the highest public spending on health resources, according to the figures released by the OECD. In the years leading up to 2014, the USA were clearly surpassed only by Luxembourg and Norway, and competed with a few other countries for rank three behind these two countries. Starting with 2014, public spending on health has sharply increased in the USA, making it the country with highest spending among all OECD countries.