How bad is using SELECT MAX(id) in MYSQL instead of mysql_insert_id() in PHP?

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Background: I'm working on a system where the developers seem to be using a function which executes a MYSQL query like "SELECT MAX(id) AS id FROM TABLE" whenever they need to get the id of the LAST inserted row (the table having an auto_increment column).

I know this is a horrible practice (because concurrent requests will mess the records), and I'm trying to communicate that to the non-tech / management team, to which their response is...

"Oh okay, we'll only face this problem when we have 
(a) a lot of users, or 
(b) it'll only happen when two people try doing something
    at _exactly_ the same time"

I don't disagree with either point, and think we'll run into this problem much sooner than we plan. However, I'm trying to calculate (or figure a mechanism) to calculate how many users should be using the system before we start seeing messed up links.

Any mathematical insights into that? Again, I KNOW its a horrible practice, I just want to understand the variables in this situation...


Update: Thanks for the comments folks - we're moving in the right direction and getting the code fixed!

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