Nice post, Zanorias
There is an art to responding to these types of issue and not accepting liability, whilst also sounding placatory and avoiding making any overt implications that the customer is actually at fault. It takes some practice though.
It's a few years since I've done anything with direct foodservice customers but IMEX they can be just as difficult as retail - you potentially replace the "I'm going to fabricate a complaint because I want some free stuff" potential with "I'm going to blame the supplier because I don't want my bar/café/restaurant to be responsible for this issue"
In this type of situation I find it difficult to avoid thinking about the probabilities of the issue. You are a manufacturing site with very limited / no glass, and that which you do have is (presumably) controlled, checked etc. Contrast that with a café where there is lots of glass, almost certainly no register / routine inspection, and if it's anything like any of the various places I worked as an undergrad then glass breakage isn't all that uncommon. Obviously this type of consideration isn't anything like a replacement for a real investigation, but it's possibly worth bearing in mind...
In your specific situation here, the point that Charles made is critical - you need evidence. Without that, even if the glass did come from your site you'd potentially be stumped in terms of actually identifying it. If they can send you the piece(s) then you can have it analysed to at least confirm whether it matches any of the presumably very limited types of glass that you do have on site, otherwise you're not really able to say a great deal on the specific piece in question.
As for the liability question, I'm not sure where you are in the world but in the UK (and probably the US) I cannot imagine any legal team advising that it is at all sensible to admit liability even when there is a reasonable probability that your business is at fault, and definitely not when this is just to appease a customer and there is no solid evidence that you may be even slightly to blame!
For now I'd simply send a letter confirming what checks you've made, outlining the systems and controls that you have in place, and reiterating that you'll be happy to investigate further if they are able to send the item in question.