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Actually, you bring up a HUGE and critical point.  I LOOOOVE the fact you look at Fister's career BABIP.  In point of fact, I myself am generally prone to preferring career numbers over stats-come-lately.
Which brings up the larger (beyond the scope of Fister alone) question of -- when is it advisable to pay attention to splits vs. career numbers?  Basically, the million dollar question is - "when is it REASONABLE to think a player has jumped to a new level?" - (in either direction).
Obviously, the smaller the data set, the more volatile and less reliable.  And, baseball has always been a game of streaks and slumps.  From Pujols to Kotchman every player will run through 1 or 2 months spells completely outside of 'normal' production.  Over time, they even out, and you get the "real" picture.
But, for "prospects" and callups -- guys with very, very short resumes, production is EXTREMELY volatile.   Smoak "seemed" to have established himself as MLB-competent before arriving in Seattle - but then spent a month making Rob Johnson look good.  As a rule, it's a sucker bet to read "too much" into any couple of months stats from a newbie.
With Fister, yes, he has a .295 BABIP in his 232 innings.  Is that a better measure for what to "expect" in the future?  It's a legit question - and there's as much art to science in the answer.
By default, I prefer careers to 'samples' - (at least until early 30s, when decline becomes a concern).
But ... with young pitchers, the ebb and flow is VERY hard to read.  So, I think you need to look how the parts work TOGETHER.  So, my mathematical take on Fister and his BABIP journey.
1) Largest sample size is his minor league profile.  In the minors, Fister amassed a career total in 421 innings with a 6.6 K/9; 2.1-BB/9, 0.8-HR/9 and 10.3 H/9.  The TTO numbers are nice enough for a control fiend.  But, the H/9 were CONSISTENTLY above what the other pitchers were throwing on his team.  And, his final 106 AAA innings showed his WORST H/9 (11.2) of his minor league career.  Zero evidence that he was solving his BABIP problem at ANY point in his minor league tenure.  (If anything, it appeared to get worse as his control got better).
2) 2009 - 11 starts at the end of the magical shoulda-been-farewell tour for Griffey.  With the #1 defense in baseball, Fister looked right at home - with a .271 BABIP (just like everyone else).  Buuuuuut ... what was his ISO for those 61 innings?  Wait for it ... 205.  He was running a .271 BABIP - but had a 1.6 HR/9.  (Small sample screws with HR/9 numbers - sure - but, of course, if it's flying over the wall - 11 times in 11 games -- it ain't counting toward BABIP.  You lauded his ability to squash power ... in 2009, when running that .271 BABIP, the enemy posted a .469 slugging average. 
So, the 2009 cup-o-joe, he was wildly off his minor league norms in BOTH BABIP and Slugging.
3) The question of "has he moved to a new level" is typically attributed to players who START poorly and finish strongly.  The idea is that they struggle out of the gate, (Smoak?), go fix something ... and then come back as a better pitcher.  It is a MUCH harder sell to suggest a player has "moved to a new level", when he has a span doing something much out of character and previous experience - and THEN reverts to performing pretty much exactly as he has before.  To *me* that is sort of the definition of streak.
4) One extra word about the 1H/2H thing in 2010.  To believe that he was "lucky" 1H and "unlucky" 2H - basically means that he pitched an entire season and NEVER actually pitched to his normal level.  For me - while I believe it is possible for a player to go through an entire season w/o a streak or a slump -- I think it would be HIGHLY unusual for a player to go through an entire season and never have a single period where he was pitching to his "normal" level.
My take:
So - for Fister, for his last 4 years in the minors, he ran horrid BABIPs with solid TTO numbers. 
He had 61 MLB innings at the end of 2009 that were atypical in nearly every aspect.
He had a GREAT 11 game start (2 months) to 2010, where he ran off-the-charts good BABIP, (but suffered a SEVERE 2.5 K drop from his minor league numbers).  You look at his April/May BABIP numbers - .241 and .234 happened while he was running 4.3 and 4.0 K/9 numbers.
When he returned, his final 3 months were:
July - .360 BABIP -- 5.6 K/9
Aug - .383 BABIP -- 7.4 K/9
Sep - .315 BABIP -- 4.0 K/9
To me, the pattern is obvious.  His BABIP is tied STRONGLY to K-rate -- but inversely.  His best BABIP performances tend to be when he is NOT striking out people. 
The stock analysis of TTO stats expects a player to get better results when his Ks rise (and his other TTO numbers remain constant).  Fister doesn't fit that mold. 
The question (in my mind) is this -- is it possible for a guy to run a 0.8-HR; 2-BB 4-K line to survive long term?  Tewksbury is about it that I can find quickly that managed to turn this profile into a genuine career.  So, yes, it is possible.
But, I would argue that the attempts to get his K rate UP have been (and will likely continue to be) counter-productive.  In the end, I think Fister might well be a guy Duncan in St. Louis could have loads of fun with.  I have little optimism that Seattle understands exactly what they have and how to optimize his usage even after seeing his usage optimized in April and May.
And this, IMO, gets to the true underlying issue with Seattle.  Player development requires agility.  You have to be able (and more importantly willing) to accept non-standard patterns for success, (or assemble talent that all naturally fits the standard mold really well). 
I have little reason to believe that Seattle will not destroy Fister in much the same way they managed to destroy Silva.  Even with the new management, I still get the sense that the organization on the whole is one of the least maleable in all of baseball.  And Z can make all the great moves he can manage - but if the standard in Seattle remains to under-perform while playing in the great northwest - the results will continue to be ugly.