In a massive simplification, a total bond index looks closest to a government intermediate bond given that government is the largest component and a weighted average of the yield curve gives roughly the same duration. If you open up Morningstar to look at total return, FIBAX and VBTLX correlate much better than FLBAX. But it is definitely not the same (see 2008) because you are missing those short and long term tails of the yield curve, and you are missing corporate exposure.
In an argument about buying an investment that correlates opposite of VTSAX (all public corporations, though obviously not bonds) it is probably fine to drop the corporate component for sake of simplicity. I wouldn't necessarily blindly trust Morningstar, but you can see they rate FTHRX two star and it clearly underperformed in the 2007-2009 region versus VBTLX and FIBAX, which is exactly the opposite of what you want out of a bond fund in the first place. Whether that is due to cost or management or whatever, it's pretty irrelevant; and I would lean on the side of simplicity rather than trying to figure out which funds are run by strong managers.
I really think if you start going any deeper to find the right balance, it's probably a waste of time. My SO has a very lousy 401K. I just explained it was fine because we are much more aggressively invested elsewhere and the portfolio as a whole is fine. It's likely we move the money into an IRA within a couple years at most so we just go with the best options for now and simplify later. So you could go into an argument about if FIBAX needs to be supplemented with other funds and technically it might; but in the end, I'm not sure it really matters too much if you're a long way to FIRE, your bonds are a low percentage anyway, or if you have assets elsewhere that can provide the correct balance for cheaper.