A new PC must meet the GM's approval to enter the campaign. A GM shouldn't let into the campaign any PC that makes the GM uncomfortable. Attempts should be made by the GM and the player to compromise so that the PC can enter the campaign, but, ultimately, the GM can—for whatever reason or no reason at all—say no to a particular character. Likewise, a player may walk away from a campaign for whatever reason, such as finding the GM too restrictive.
Anyway, that said, here the FAQ agrees with the player in the following exchange:
If a PC has an item crafting feat, does a crafted item count as its Price or its Cost?
It counts as the item's Cost, not the Price. This comes into play in two ways.
If you're equipping a higher-level PC, you have to count crafted items at their Cost[s rather than their prices]. Otherwise the character isn't getting any benefit for having the feat. Of course, the GM is free to set limits in equipping the character, such as "no more than 40% of your wealth can be used for armor" (instead of the "balanced approach" described on page 400 where the PC should spend no more than 25% on armor).
If you're looking at the party's overall wealth by level, you have to count crafted items at their Cost. Otherwise, if you counted crafted items at their Price, the crafting character would look like she had more wealth than appropriate for her level, and the GM would have to to bring this closer to the target gear value by reducing future treasure for that character, which means eventually that character has the same gear value as a non-crafting character--in effect neutralizing any advantage of having that feat at all.
So, in short, the player's not wrong in his desire for his PC to benefit from this ruling.
However, it's possible that the player may be trying to maximize his PC's use of the feat Craft Magic Arms and Armor by, like, using Table: Estimating Magic Item Gold Piece Values to devise new magic items that also just so happen to be armor or weapons and having his new PC enter play with—at cost—an at-will command word-activated +1 sword of cure light wounds, or adding existing magic items to armor or weapons and saying that the entire +1 sword of holding ("It's a +1 sword! It's a bag of holding! It's both!") has been created using the feat Craft Magic Arms and Armor alone and is therefore available to his PC at cost.
If that's the case, you really don't have to approve those new or unique magic items. (And, in fact, you can veto the PC possessing any magic item you think will create problems or that's inappropriate for the campaign.) You can also mandate that the player's PC limit himself to buying or creating for cost printed items. By the way, if you do limit this PC this way, it's only fair that other new future incoming be limited likewise.