You user may be confusing the 2mb limit to the upload limit that phpmyadmin has. It won't let you upload more than a 2mb file. If you want to import a database bigger than that you will have to use the command line, but databases are in no way quota limited except for the ammount of space the user has.
MySQL does not have a quota system so there are two ways to go about limiting MySQl database sizes.
Put a quota limit on the MySQL data directory. Unfortunately this limits all databases to tally up to the quota. (not a good idea)
Or, a better way is to create a php script that is run every so often, adds up the table usage for a tally on the database and if it is over the ammount you specified you can have the script remove insert privileges or something. This way it is on a per database (or user) level depending on how you set it up and the user is still able to login and free up space instead of being locked out completely. The next time the script runs through it will not whether the table has had its privileges removed and if its back under its quota limit, reinstale insert functions.
This is the best method at this time to put quotas on MySQL databases.
In general, it would probably be better to leave it as is since it is the users space that they paid for to begin with.