Is Running the Ball Really "Safer"?

Conventional wisdom dictates that rushing the football is a "safer" option than passing due to a lower risk of a turnover. However, does this increased security justify the decreased expected yardage compared to passing? 

To start, I looked at the average yards gained per attempt for rushing vs passing, based on the 2014 NFL season.

Type	Rushing	Passing
Yards	57002	121247
# Attempts	13688	17879
Yds/Attempt	4.16	6.78

Data from Football-Reference

Note that this is over all passing attempts, not just completions. Even taking into account incomplete passes (which gain 0 yards) and negative sack yardage (which, in NFL, are deducted from passing yards), passing the ball clearly gives larger expected yardage, by 2.62 yards per play. However, the threat of an interception means rushing is "safer"... right?

Fumbles occurred on 4.89% of rushing attempts, while interceptions occurred on 2.52% of passing attempts. However, the offense can recover a fumble, and does so 37.9% of the time on rushing plays, with the defense recovering the other 62.1%. Factoring this into the above figure means 3.04% of rushing attempts result in a turnover. 

Type	Rushing	Passing
Attempts	13688	17879
INT/FUM	670	450
Turnovers	416	450
TO Rate	3.04%	2.52%

So in the end, rushing is MORE risky turnover-wise than passing (or at least it was in the 2014 season).

This doesn't mean teams should pass the ball 100% of the time: there's still game theory to be considered. However, the above results counter conventional wisdom, and imply that teams are both leaving yards on the table AND are risking more turnovers by running the ball too often.