Can oats, grasses or any other plants host the rust that infects our garlic crop? I grow about a half-acre of garlic annually and we deal with rust pressure every year, using integrated management to keep it relatively at bay. I want to grow oats and possibly explore other grasses for cover crop options (we currently overwinter a rye/clover mixture). I have been told that these grasses can worsen our rust problem. However, upon further investigation, it sounds like garlic rust is host specific.
Thurston County Washington garlic diseases
While I am not a pathologist (just an entomologist), I do have access to some good references on garlic including a Compendium of Onion and Garlic Diseases and Pests by H. Schwartz and K. Mohan. In this book, Puccinia allii has been found on most Allium spp. including chive, garlic, leek (wild and cultivated) and bulb onions. I would conclude that a grass cover crop would not worsen the rust problem by serving as an alternative host.
I would encourage you to review the chapter on Garlic rust in the PNW Plant Disease Handbook where real pathologists talk about cultural and chemical strategies for reducing the incidence of rust in garlic. https://pnwhandbooks.org/plantdisease/host-disease/garlic-allium-sativum-rust
The only drawback that I can see is if the cover crop (rather than a rotational crop) reduces the movement of air within the canopy of the garlic. It does appear that excessive moisture in the form of leaf wetness could exacerbate the appearance of rust in your garlic crop.
Hope this helps! Good luck in your endeavors.