NO! They're directly affected by how many runs they allow batsmen to score. Bowlers are in control of their own destiny, and consequently the game.
Bowlers are affected by decks (some more than others); batsmen are affected by how well bowlers bowl on decks. The bowler controls the game, though better bowlers need less assistance from the deck to control the game.
The idea that any number of batsmen suddenly got miles better at the exact same time, in the 2001/02 season, is, to me, nonsensical. That supposition simply misunderstands how the game works. It makes far more sense, looking at how the game works and what happened (ie, the number of flat decks increased massively, almost overnight; any number of once excellent bowlers either disappeared instantly or had a few terrible games then disappeared), to conclude that batting got a lot easier very quickly in 2001/02.
People who are fans of the batsmen in question naturally don't like this supposition, but to me it's the only notion that makes sense. No-one is saying the likes of Ponting and Kallis for instance did not get better than they had been up to 2001, merely that the extent to which many batsmen got better has been exaggerated by the fact that batting got easier, and the fact that some batsmen's weaknesses were not able to be exploited after 2001/02 meant some batsmen who could easily have failed completely up to 2001 succeeded, sometimes very well, after 2001/02.
Mohammad Sami doesn't allow Tendulkar to score runs, he has no choice because he is no where near good enough to combat him unless Tendulkar makes a mistake. Batting averages ARE directly related to bowling averages, unless you have a way of making wickets and runs magically appear from no where.
You said it yourself, bowlers are affected by decks. Bowlers can't take 5/23 on decks like Napier or some of those rather interesting Indian pitches. Bowlers don't control the game, umpires or Ricky Ponting do. Batsmen can also bully the bowlers.
Correct, batsmen did not all of a sudden get better, though I do argue that by luck we do have a higher quality of batsmanship across the field atm (just like some eras have more good bowlers than batsmen). I never said all the current 50+ batsmen were all time greats so please don't put words in my mouth or I will have to be very nasty to you. I do think players like Yousuf would still average in the 40s however because there is nothing wrong with him technically, though he can be prone to short pitched bowling. Ponting would hardly be affected at all, likewise Kallis, Dravid, Tendulkar and even your favourite Sehwag. Their averages would be lesser if they batted on more greentops, how low depending on the amount of greentops. They still remain good batsmen. Plus if the conditions changed how do you know they would not change their techniques to suit?
The pitches also got flatter, influencing batting averages AND bowling averages. The good bowlers did not "disappear", they were hampered by the conditions because no matter how good you are, a road is a road and you can't roll teams for 120 on them unless that team is NZ with a massive injury list (well okay, just Taylor, Ryder, Vettori).
So yes, batting is relatively easier in the 2000s. That means an average of 25 for a bowler these days means more than an average of 25 in the 80s. You cannot have it both ways if you want your theories to be logical.
Lets take Iain O'Brien in his final test as an example. He averages around 33, so a solid bowler. He was bowling at 145+ and is naturally a bowler that gains a lot of bounce and seams the ball. Pakistan are awful at this point against bounce and seam movement. He was bowling at Napier and went very unrewarded in the second innings, though in the first he was excellent.
If that pitch had been more bowler friendly I think it would have been exploited more. Hence the likes of McGrath, Pollock, Warne, Bond and Steyn having the records they have is outstanding. They have bowled in one of the most batsmen friendly eras ever so if we're going to start taking runs off batsmen, then I think we can make bowling averages lower unless you want a mass run out fest, which has nothing to do with batting technique.
Also, do not assume I am a batsman fan. I am a legspinner who cannot bat to save his life. You're not the only bowler in the world.
So please, lose some of the prejudice or at least apply logic to your theories. You won't of course, you'll eventually have the last word in this discussion and assume you've won.