Hello my name is XXXXX XXXXX I will be happy to assist you.
I am very sorry to hear that you are this mugshots website. I have worked with other people before who had this problem.
First let me explain to you what google is and how it works so you better understand your situation.
Google is a search engine that provides relevant results to to users when web sites match the terms entered into the google search. Google does not hold that data that you are seeing, the website does. Google simply indexes the websites and points a link to the web page where the terms are matched.
So the in your case your issue is with the website and not google.
Unfortunately google will not remove the search results unless your personal information like social security number is XXXXX
As they told you at mugshots.com they cannot guarantee that the mugshot will not show up elsewhere because any number of websites could also list your name.
So really you have 2 options, you can pay mugshots.com for removal or you can bury the information. I am sorry but there is no way you can remove something completely from the internet, if there was than no one would have bad information about themselves online. This is the reality of the situation unfortunately.
Basically in order to bury this page you are going to need to get as much positive information about yourself online as possible. Some examples would be to create a new website for yourself with a lot of content and articles about you, using your full name.
Create a free blog , create a public facebook page, create a twitter page, pretty much get yourself on all of the big social media websites.
The search engines are going to connect your name to what is out there so the more positive information that is out there and updated regularly the better chance you will have of burying this page.
I will tell you flat out it is going to take weeks or months to do this. The method I described above is most likely the same method the company you spoke to would use however that price they quoted is very high.
I wish there was an easier way but unfortunately this is one of the downsides to the internet, things can be found forever and there is nothing that can be done other than making it a bit more difficult to find in the first place.
There is no way anyone at google can just bump the page down. If this was the case then you no one would have any negative information listed in google. The only options are to either get the page deleted from the website OR try to bury as deep in the results as possible.
There are many services out there that you can pay to help you with this, I cannot say how good a job they do you may want to give them a call and see if they can help, have a look here:http://www.reputationmanagementconsultants.com
And here is another:http://www.reputation.com/
I believe they both provide free consultations.
As I said though if you have the time and the technical know how you could possible take care of this yourself or make it harder to find.
Again I am very sorry about this situation, I stand strongly against these types of websites and think they should not be allowed as they are essentially punishing someone forever for something that was done in the past. Until there is a law about it then I am afraid they have the right to display this information.
I hope that this information helps you. I would kindly ask you to remember when you are asked to rate my service you are rating me personally. You are not rating the mugshots website or their procedures or your frustration with the situation which I know is difficult.
If you need further clarification please let me know.