This is just based on ignorance of stats, your hypothesis makes zero sense especially since the best playmaking safeties have always produced strong counting stats (unless you want to just boil water ed reed's exceptional PD's and INTs last year to his getting picked on lol). He's a ballhawking safety which in today's NFL is >>>>>>>>than a safety whose forte is run stopping. We are already a good run stopping defense and running is nowhere near as efficient for offenses as passing is.
But anyway, some background on the following statistics:
Advanced NFL Stats Player Statistics
Now, here's where byrd ranked last year in these categories:
1) +WPA - 4th (1.49)
2) +EPA - 5th (46.1)
3) +EPA/G - 7th (2.88)
4) SC - 13th (40)
Note that the last one is a counting stat that puts him in the top echelon of starting safeties and is the stat which is most reliant on teammate performance. It is simply impossible to show up so universally positively in these stats AND have the counting stats simply because "you are getting thrown at because you aren't covering your man." Your analysis doesnt make any sense and it makes even less sense considering how bad the secondary as a whole was/is.