[shakermaker]

Here are the amount of penalties awarded against teams in the Premiership, from the start of the 98/99 season to the start of the 08/09 season. I can't find earlier stats, but a ten year slice seems fair to me. The nine teams listed are the only ones to have been in the Premier League since the start of the 98/99 season.

1. Manchester United: 18 (8 home, 10 away) % at home: 44.4
2. Arsenal: 23 (8 home, 15 away) home %: 34.8
3. Chelsea: 29 (8 home, 21 away) home %: 27.6
4. Liverpool: 32 (11 home, 21 away) home %: 34.4
5. Middlesbrough: 37 (16 home, 21 away) home %: 43.2
6. Everton: 39 (16 home, 23 away) home %: 41
7. Newcastle: 44 (15 home, 29 away) home %: 34.1
8. Tottenham: 48 (18 home, 30 away) home %: 37.5
9. Aston Villa: 49 (16 home, 33 away) home %: 32.7

From that data, we can see that the statistical probability of a penalty being awarded against Manchester United, Arsenal or Chelsea is very low. That can't be disputed.
Indeed, we also see that Manchester United hold the highest percentage of penalties conceded at home. Personally I don't see the importance of that particular statistic when the overall amount of penalties over ten years is only eighteen.
I think the state of low probability is because the performance of referees, and you think it's because the best teams simply don't allow the opposition to get in their 18 yard box very often. A simple difference of opinion. I respect yours, but it seems that we're going around in circles.
Cheers for the discussion.