Is spontaneous combustion a real thing?

Yes, the most common example is wet haystacks as they dry out. The wet hay ferments (similar to compost) causing it to heat up, but when the surface drys enough sometimes the surface ignites from this internal heat. This can be a major loss to a dairy farmer or a rancher.

Piles of wet and/or oily rags can do the same for the same reason. This is a common cause of household and industrial fires.