I've paid my rent late a few times, but never more than 3 days late. However, someone told me that even 3 days is enough for them to go report it to the credit bureaus. Is this true?

Not one state mandates a grace period. The only time a grace period is allowed is when it is written in the lease.

If rent is late by even one day...it can be reported to the credit bureaus and the landlord can start eviction proceedings.

i don't think so... usually you have a 10 day grace period as long as you don't repeatedly abuse it.

READ your lease.
Mine says rent is due on 1rst and LATE after 4th.
Most LLs only report tenants who stiff them, not anyone 3 days late.