What was Debt Burden in 2008?
If by 'debt burden' you mean total US public debt, then according to the CEIC somewhere around 750% of US GDP.
When I look at a different source, I don't see anything at 300% in 2008. https://fred.stlouisfed.org/series/GFDEGDQ188S
What's going on?
Fred data you cite use total federal government debt (see the notes). That is not equal to total government debt. Total government debt would include debt of all other government organizations at any level not just federal debt.
However, according to the published numbers I found Dalio was still incorrect. Data provided by CEIC show that the total US government debt was somewhere in ballpark of 750% of GDP (see the graph below).
The YouTube video does not have references to the data used. It is possible that Dalio used different definition of total US government debt than CEIC. Perhaps he only took into consideration US Federal and State governments, I do not see it anywhere explained in the video. Alternatively, the data could have been revised since (the video is from 2013, data do sometimes get revised after publication). Unless Dalio somewhere provides more details we can only conjecture why the number is different from the one provided by CEIC.