
The "round to even" does NOT produce a bias
"Having spent several years studying physics..." Well, I have a degree in physics (Bachelor, and some graduate school work towards Physics PhD). Also, I know basic statistics.
"Always rounding to even numbers produces a bias towards them and brings in an additional inaccuracy." The only way you can say that is if you know that your original numbers (to some chosen significance) tend to be odd. Do they? No, they do not. On average, you are just as likely to get even numbers as you are to get odd numbers for a given range of possibilities. Thus, if you then follow the rule to "round to nearest even for numbers EXACTLY between two digits" you will NOT have a bias. If you instead do as suggested here (and in elementary school) and round upwards, you will absolutely introduce a bias to larger values in your data. For more, read the Wikipedia entry (look under Statistician's Method, which is what scientists who wish to have nonbiased data would use): http://en.wikipedia.org/wiki/Rounding (note the phrase "This method is sometimes known as "round to even" and is used in order to eliminate the bias that would come from always rounding a number ending in five up every time." in particular.)
The "round to even" does NOT produce a bias
0 is a digit, as is 1,2,3,4,5,6,7,8,9. Count them. Yup, there is 10 of them. Rounding up on 5,6,7,8,9 gives 5 chances to round up. Truncating on 0,1,2,3,4 gives 5 chances to truncate. It is a lazy analysis which states that "rounding up on 5 introduces a bias".
The "round to even" does NOT produce a bias
To say this is a lazy analysis while providing such a flawed analysis is impressive. If you sum the changes from 04 rounding down and 59 rounding up, you get 0 + 1 + 2 + 3 + 4 for rounding down (total 10) and 5 + 4 + 3 + 2 + 1 for rounding up (total 15). On the other hand, if you round to even, then the total changes for rounding down is 0 + 1 + 2 + 3 + 4 + (half of 5), and for rounding up is (half of 5) + 4 + 3 + 2 + 1, which you will note is 12.5 for both.
Round to even changes the distribution
To be honest, I don't trust Wikipedia to be terribly accurate, so I went and tried a few more trustworthy mathematical sites and they seem to say the same thing. I must confess that I'm quite surprised by that. If you take a distribution of random numbers, it should be fairly flat: 
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