Like you found out, they can't. A number of diseases can have mouth issues and intestinal issues (intestinal tuberculosis for example). The reason they do biopsies is to check for possible granuloma (not always present, but if they are it's a good way to differentiate between intestinal TB and crohn) and they can do a few ELISA tests on the biopsy to differentiate between crohn and other infectious diseases.
The biopsy is not meant to check if you have inflammation or possibly crohn, they can see inflammation through blood screening, but the biopsy is meant to differentiate between other possible candidates like TB.
Many researchers are interested in mouth ulcers related to crohn though, since there are a number of ways that ulcers form, some form from the inside out, some from the outside in. If you would swallow something very acidic, you could get a mouth ulcer, that's an outside in mouth ulcer (the substance came from the outside and created the ucler inside your mouth), but if you have a bacteria, and develop mouth ulcers, that's an inside out mouth ulcer (the bacteria was present in the body and created inflammation from the inside which had clinical effect on the outside, your mouth). There is a study that tried to find out if crohn is outside in or inside out.
Why this inside-out, or outside-in, is important is to know if the body is promoting the inflammation through T cells on their own, or if some substance or bacteria on the gut lining is promoting inflammation in crohn's disease.
