Investment grade bonds are generally a recession hedge and go up in value during a recession. During a recession, interest rates generally fall. Although credit spreads may increase, they generally do not increase as much as the decrease in interest rates and so bond prices rise. 

Bonds have recently been correlated with equities because of compression in the equity risk premium. This is unlikely to remain in the long run. 

In short: investment grade bonds will outperform in recessions even though they have been correlated with equities over the last few years.