Your question is a bit too vague.
The very short answer is:: Don't do it. That you are asking here means you probably don't know enough to do it right.
The slightly longer answer is:: The technicians are wrong. It can be done.
mmm. A more comprehensive answer.
- Can you use a database on another server for your WP?
Yes you can.
- What do you need to do?
Well, you need to set up the {database server} to accept connections from users on anything other than localhost. This has to be configured on the {mysql database SERVER}. You then need to create a database user on that server with privileges to log on from a different IP address. That is the database user you will use to connect to your database.
-Should you do it?
Probably not. When not done correctly, it introduces a whole raft of security issues. You get bonus points by leaving the database server untouched, but enabling SSH access (which you should already have on a dedicated server btw). You then create an SSH tunnel on your {WP Host Server} that redirects all database queries, via SSH to your {database server}. Your {database server} still sees those queries as localhost, so no changes required there. One of the benefits of SSH is secure connection between the {WP server} and the {database server}. Trying to use web admin panels to set up your database server introduces yet another layer of abstraction, and potential security holes. If you are not comfy with the command line, you probably should not do it.
-No really, why should you not do it?
Another issue is that it can introduce a performance hit. Think about it. To serve a page, a visitor visits your {WP server}. That then queries the {database server}. Only when it has received the result of those queries can it serve the pages. If the link between the {wp server} and the {database server} is a slow one, your whole website is slow. Plus, you have just doubled the amount of traffic passing through your {WP server}. YMMV but in 99% of the cases, this could end up being the bottleneck. You can of course use aggressive caching plugins and techniques to reduce the number of queries to the DB.
- Can you use one database for many WP blogs?
Yes you can. Easily. Just set a unique table prefix for each blog's installation. So, while sharing 1 database, each blog has effectively a unique set of tables so is totally independent. This is a hangover from the days when webhosts would limit the number of databases you could have on your hosting package. So, if you wanted more databases, you either upgraded the webhosting package to big $$, or you used table prefixes to keep each blog separate. Such a setup has its advantages, and some disadvantages too, so YMMV. I guess though, that this is not what you are asking ...
- But I want them all to share the same underlying data ... can this be done?
Yes it can.This is where you have start poking with the PHP in WP to override the two database entries that WP has for the original site address and home index page. This page is a good start and shows how it can be done easily
http://codex.wordpress.org/Changing_The_Site_URL
Not doing this, or changing the entries in the database is why as you put it, "the broser jumps to the url of the original blog that has that db on a local host". If you permanently want the DB shared by multiple blogs, it is a bit more involved than this, but I hope you get the hint.
One more thing you need to watch out for, is plugins that do not play nice with such a setup, and insist on writing and hardcoding the URL in their database tables. Again, you will need to override these plugins individually. One more thing. All your blogs will need to share the same template. At the very least, they need to use a template called the same thing. It gets messy when you start using widgets different templates sharing the same name across several blogs. Needless to say, depending on your specific needs and usage, it can get pretty ugly pretty quickly just trying to stay on top of all the customisations. For the most part, you will have to say goodbye to one-click upgrades too.
On top of all that, you have now introduced one point of failure for all your blogs that share that database. When ('when', not 'if', if you stick around the web long enough), your dedicated database server goes down, your entire farm goes offline. If you have several blogs depending on it, you had better have a pretty good data backup, and more importantly disaster recovery plan.
Hmm, I could go on, but back to your original questions ..
-Can it be done? Yes
-Should it be done? Probably not. Whether you decide to have the WP installs share a database or not, you are probably better off just moving the blogs to the dedicated server that has the DB. Depending on how often your database changes, or new content is added, you might also get better traction from periodically replicating the data than from having multiple blogs share one database.
I do understand that there are other considerations .. like separate IP addresses of the blogs for SEO, but if you do do it, at least know about the potential downsides as well.
/J