• There's a lot of attention being paid to oil right now
• There have been moments of correlation between oil and bond yields
• How much of the relationship is 'causal' vs incidental?

Oil has certainly been on a rampage since late 2014, moving quicker than any of the other major markets that we track for the purposes of bond market analysis (the pace was similar to Greek credit spreads during Greece's near-collapse).  Like the Greece situation, any time any major market moves that quickly, there's a tendency to give it too much credit for moving other markets, like bonds/rates.  

To be very clear, both Greece and oil did actually have a big impact on other markets (oil continues to have an impact, obviously).  The point is that the correlation is not "always on."  Bonds aren't transfixed by oil prices, although they may take cues from each other intermittently.  At other times, the correlation ranges from questionable to completely inverted (like March 16th and 29th after FOMC and Yellen, respectively).  If we look at the bigger picture, we can see that European bond markets started this whole affair with a break to all-time low yields before oil ever broke 2014's lows (bottom pane of the chart).

In terms of the 'variety of reasons,' of course there are oil-specific motivations for the lower oil prices, but keep in mind that many of those explanations have come about AFTER prices began to fall.  All too often in financial markets, the price of a particular asset will begin to move in a major way and then market participants rush to explain/understand.  Some of the logical explanations behind the oil move make sense (oversupply, of course), but it's not as if the world just woke up one day and suddenly realized there was an oversupply problem that no one saw coming.

Bottom line: yes, traders are keeping an eye on oil prices and yes, they can impact bond markets.  But oil isn't any more a permanent motivation for bonds than stocks.  And if you ever need help remembering how much the correlation between stocks and bonds can vary, just look at the long term chart of the Dow vs the 10yr.