i think the problem with these kinds of stats is the sample size is ridiculously low in some cases (like the "last possession to take the lead or tie" clutch stats). the "less than 5 minutes, within 5 points" stats have a larger sample size, but usually isn't what most of us are talking about with "clutch", as in "game on the line during that possession". which are usually the more memorable moments, and the reason we cling to them.
i think part of the LeBron thing is that while his "last 5 minutes, within 5 points" stats are very good like you said, his "last possession" stats aren't. or at least, from stuff i've seen. i remember seeing an article earlier this year that said he was like 2 for 25 from three in those situations over the last 5 years. which is probably why i have an image of him jacking up bad threes at the end of games.
note: the more i look at the last 5 minutes stats, the more i think LeBron is unfairly treated (by me too). and it seems the story of how the Heat chose Wade as their closer at the beginning of the season turned out to not have an impact on the actual season lol.
overall, you are right in that this is a case of what "seems true" vs what "is true".
So I'm going to put together the numbers for the ten guys with strong clutch reputations (plus James) for the past 10 years (2002-2003 through 2011-2012). For definitional purposes I considered a last possession shot (I've included playoffs and regular season together) a shot with less than 24 seconds left and that shot ties the game or gives the lead to the shooters team (obviously this doesn't account for shots at the end of the game that put it out of reach which can be as important or FT).
So with that limited definition here are their orders in the following categories.
Comment: Well Bryant is by far the champion shot taker (although he does have an extra year of shooting them on Lebron). But Lebron is a good seven takes clear of anyone else. In his relatively short career Durant has taken an insane number of these shots. Paul is the only one in this look under 50 attempts but I think he is a great clutch player in really underrated ways so I wanted to include him.
Comment: Yet again Kobe leads the pack by a lot. Durant has an insane number for his age. Billups, Allen, and Durant have taken over half of their ultra clutch shots from 3. Dirk and Melo would take surprisingly few threes based on what you would expect given their reputations.
Now we'll look at makes.
Comment: Again Kobe leads the pack by a fair bit but given the number of attempts he has that's not surprising. Melo grades out really well on makes (remember he has the second lowest number of attempts after Paul). Lebron acquits himself fairly well in makes overall tying with Dirk (of course he also has a bunch more attempts than the guys around him. Allen does pretty well too. Durant has already passed Wade, Pierce, and Billups despite their significantly longer careers. Billups has a real paltry number of makes.
Comment: Allen leads the pack in makes despite being behind Billups and well behind Kobe in attempts. Durant again has made a ton for his age. Billups, Allen, and Durant all have over half of their makes as 3 pointers. Paul rarely attempts 3s so his result is not surprising.
And now the efficiency stats
Comment: As everyone probably already knows everyone shoots poorly in the clutch pretty much even the best players. Melo is the only player who shoots relatively normally in these situations (in fact that may be higher than his overall career percentage). Their are varying degrees of bad though. Paul, Dirk, and Allen are quite good in the context of these shots where the league in general is pretty bad. Durant, Kobe, and Lebron are below league average but not awful given the quality of defense they face. Wade, Pierce, and Billups are horrible particularly Mr. Big Shot who is one of the worst in the league overall (I'll explain how he got his name later).
Comment: Allen and Melo put up great numbers here (league average I believe is in the 2s on this). Their numbers would be good for 3 pointers in any context. Ray Allen in particular has a ridiculously gaudy number. Given these numbers Melo should probably take a few more 3s and Allen can keep firing away. Billups redeems somewhat his awful overall percentage with a pretty effective 3 point%. Durant's is pretty high too especially given his penchant for high degree of difficulty shots. Bryant shoots pretty poorly but probably about average for these situations. His 3s are probably more effective than his off balance 2s though. The bottom five really don't have much business taking these shots. Paul only takes a couple every year so he gets a pass. Dirk has basically stopped taking them at all recognizing it as a weaknesses and something he gets guarded on. Pierce did a lot more early in his career but has cut them down as well. However, Wade and especially Lebron WTF are you doing taking these shots.
From this it quite clearly emerges that Melo and Allen are the two best ultra clutch players in the league. I'd pretty much 100 times out of 100 have them take the shot than Kobe especially from 3. Paul doesn't shoot very much but when he does he's quite effective. Dirk and Durant put up good showings (Durant started his career very good had 2 years where he took a bunch of bad hero shots but seems to have righted himself this year). Kobe is definitively not as clutch as these five players. Only way I want him shooting instead of Dirk or Paul if its a 3. I don't want him shooting at all over Durant, Allen, or Melo. Kobe is definitely average from an efficiency perspective but given the defenses he faces we can call him above average in the clutch. Billups has an incredibly inflated repuation (based almost entirely on 2002-2003 where he was 6/12 and 5/8 from 3). Wade and Pierce are both horrifically bad ultra clutch players. The idea that Wade needs to be the closer over Lebron is fucking silly. Lebron's numbers have really taken a beating from his Miami days. I think as people started to say Lebron you need to take over more he started taking dumber shots verses doing what he used to which was let the shots come to him.
Btw worst performance in any given year from any of these players? Easily Pierce's 0-14 year from 2002-2003 (dishonorable mention Billups 2003-2004 2/19 2/11 and Kobe's year this year 3/18 1/8). Best performance? Melo's 8/14 2/3 2005-2006 was strong especially from an efficiency perspective but it has to be Durant's absurd 10/23 4/12 this year. Only player to make double digits on this type of shot in one year and still had reasonably good efficiency. Allen's 2008-2009 was pretty absurd too with a 6/9 6/8 line.