Old tires pose 3 primary environmental risks, chemical, disease, and fire. Tires are not just rubber any more. They are better described as petrol-chemical plastics. As such, they break down over time and can release petroleum chemicals into the soil with some heavy metals. While the release is slow, it can build up over time and possibly be absorbed by vegetables and plants.
We are always concerned about mosquito growth in tires. A very small puddle of water can produce a lot of mosquitoes, which are vectors for several diseases. A tire would need soil placed very carefully to avoid becoming a mosquito breeding site.
The fire issue seems small for a single tire in the landscape or even a small group of tires. In a wildfire situation, they can still pose a pollution risk to the soil and the air.
Instead of planting in old tires, try container gardening.
References:
Wideman, F. (2017, January). Planting in Old Tires. Retrieved from https://ask.extension.org/questions/381169