"Natasha's enhancements are compliments of the Red Room, not SHIELD. Whatever they did to her is lost to her fabricated memories and the burning of whatever she left behind." And Clint was not about to break any confidence Natasha had with him, be it her slightly jumbled past or her few shared secrets. Those were Nat's to tell in time.
"When and if required, agents are occasionally administered treatments that may or may not cause side effects that are similar to the serum. We all know about it, it's in our contracts." Because a SHIELD asset was a SHIELD asset and SHIELD took any measure needed to keep it's assets alive. Even if that meant experimental drug or toxin use.
"The Infinity Formula, which is what we all think Fury is full of, since he's like ancient or something, was fabricated with samples of the serum to work with the body and help boost things like strength, speed, healing, slow down the aging. All that fun stuff." Weaving through traffic, only marginally bothering with things like stop signs or give way crossings, Clint took the long way around the city, heading towards HQ.
"We're not read in on everything, some things are Eyes Only, or just classified above our pay grade, but most everything is logged on the system somewhere."