I wish I could find good tires for $100. Last time I bought tires I spent around $1200 for the set.

As for Schwalbe, I've used 26 x 1.75 SMP, 700 x 25 Durano, and 700 x 25 Ultremo tires all without a problem. The only manufacturing issue that Schwalbe ever recalled tires for was a batch of Ultremos (IIRC) that had a weak section that blistered and blew out. Of course, for any product, manufacturing errors can occur and slip through the QA (quality assurance) process. This is what the warranty coverage is for.
As a former manufacturing engineer, let me explain the process: Let's say Schwalbe makes 5,000 of their Big Apple 2.0 tires in a production lot. They're not going to mount and caliper test each and every one of them since they have a certain degree of trust in their production machinery. That degree of trust is expressed in the QA testing scheme. For an established process with a high degree of trust, a company will likely use an ANSI Z1.4/ISO 2859 sampling plan. Tires would be non-destructively tested, so (most likely) a "Normal - II" sampling level would be used to determine how many tires out of that batch of 5,000 will be randomly checked for failures. Per the sampling tables, QA testing would randomly select 200 tires to test for various attributes. Assume they're inflating them on a rim and checking for radial and lateral true within a specified tolerance of +/- 5.0% (which would make your 0.125" issue fall Out Of Spec by +1.25%). A manufacturer with a high quality assurance level will rarely use an AQL (Acceptable Quality Level) weaker than 1.0%, meaning that 1 out of 100 items are allowed to fail specification. Assume Schwalbe is running a very tight ship and they use a 0.25% AQL, meaning 1 out of 400 items is an allowable failure. Of the 200 tires selected for testing, if 1 fails, then the production lot is considered passable. If 2 fail, then the entire lot of 5,000 is considered failing and the failure mode is subject to departmental review before determining if the failed attribute is truly a reason to scrap the lot. (e.g. A 6.25% wobble would be a true use failure as outlined here. A crooked sidewall label might get let through if it's not deemed too far OOS).

SO, long story short: Schwalbe probably only looks at 200 of every 5,000 tires they make. 4,800 of them just go into a box and get shipped out. It's possible that there are 13 of those 4,800 tires that have problems, and you might have gotten one.
Don't badmouth the company for it. Follow your warranty procedure and get your replacement/refund.

Disclaimer: The numbers above, with the exception of those related directly to the ANSI Z1.4 sampling attributes, are completely pulled out of my arse. I have no idea what Schwalbe's actual QA testing policy is. This information is for example only.