Lewis, I rarely get complaints. Last one I had was a very apologetic customer asking me to come back and have a look at a rug (dead cheap one, always the way) that had buckled when drying (we left it hanging over a rail to dry). They were quite friendly and understanding, almost sorry to call me back. These are GENUINE complaints and get handled without compromise, to ensure the customer is happy and will return next time rather than have a bad experience and go elsewhere in the future.
The complaint I had before that was a landlady who decided her rental property was costing too much to fix, after the last tenants did a bunk and left rent arrears to the tune of £1k. She thought she'd have the carpets cleaned and complain to avoid paying for it. She didn't bank on dealing with me though

I'm pretty sure Craig runs his business in the same way as me, so will handle complaints very similarly.
The "complaint" he's described above is NOT the genuine type of "sorry to bother you but could you come back and have a look at this? we don't think it's quite right" complaint. It sounds like the classic professional complainer who are aggressive in their complaint, will not take any form of offer to settle the problem or re-clean... they just want to avoid paying the money.
Unless you are even more stubborn than me, forget it, otherwise county court claim... no pi$$ing about, as soon as they say they are not going to pay it you play hard ball put the claim in.