Your deposit requirement was NOT based on the previous tenants inability to pay their bills. The deposit requirements are listed at the end.
For the deposit you are required to pay either you did not agree to participate in the ONLINE credit scoring process(1), you did and they determined you to be a high risk(4), or you had other issues such as YOUR unpaid bills(6) or a bad SSN(7). Basically all of those are saying that you are a high risk, so they will charge you two times the highest months usage over the previous year. Fair or not, this is the best gauge they have as to guess the approximate usage. Just like when you move out they will use your usage to determine the next tenants deposit(if required).
If you did the ONLINE credit scoring process and got considered High Risk, perhaps as was stated before things that you thought were unnecessary were actually necessary.
http://www.murfreesboroelectric.com/residential/deposit.pdf
Residential Service Applicants
1. The standard deposit amount for residential customers shall be $300, or an amount equal to two times the highest month’s usage for the service address during the preceding twelve months, whichever is greater, unless the applicant chooses to participate in the ONLINE credit scoring process. The deposit may be reduced based on credit score of the applicant as determined by the ONLINE Utility Exchange.
2. New-service applicants who pose no credit risk (Green Light returned on ONLINE Utility Exchange) will be charged no deposit.
3. New-service applicants who pose minimal risk (Yellow Light or "No record" returned on ONLINE Utility Exchange) will be charged a deposit of $150.
4. New-service applicants who pose substantial credit risk (Red Light returned on ONLINE Utility Exchange) will be charged the standard deposit equal to two times the highest month’s usage for the service address during the preceding 12 months or $300, whichever is greater. If the service address is new and has not had service before, $300 shall be charged.
5. Any existing customer who has no deposit, or who has less than a standard deposit, and who has had two or more delinquencies or returned checks or a combination thereof in any consecutive 12-month period, shall be deemed to have an unsatisfactory payment record and must pay the standard deposit, an amount equal to two times the highest month’s usage for the service address during the preceding 12 months or $300, whichever is greater, to continue service.
6. A customer who has an unpaid utility bill at another utility according to the ONLINE Utility Exchange shall pay the standard deposit equal to two times the highest month’s usage for the service address during the preceding 12 months or $300, whichever is greater.
7. A service applicant who provides a social security number that is returned as deceased, nonissued, belonging to a person under the age of 18, or belonging to a person other than the applicant, or is fraudulent, shall be required to provide a valid social security number as well as additional proof of identity i.e. valid drivers license, Social Security card, etc. before service will 2 be activated using the ONLINE Utility Exchange. If the applicant is unable or unwilling to do so, the standard deposit shall be charged.
It probably was based on their usage, and "excessive" is very subjective. If for example they used $850 in electricity a month, then that is the usage they will base it on. Fair or not, when you leave they will base the next tenants usage on what you used. But I think it also may be based more on your history than you are willing to believe.
I have never had a problem with my utility bills, maybe not perfect with my other unnecessary bills, but utilities have always been paid on time.
IF you are saying that they did not base it on your Credit Report. What does your previous utility company say? If you call them up and get a statement from them showing you always paid on time, that may be enough for them to waive the deposit(or at least lower it).