In case of asylee the AOS decision is backdated to 1 year from the actual date the GC was granted (and that backdated date is included into GC in the "residence sinse" row). So, you can apply for naturalization 4 years and 9 months after that date, or, what is the same, 3 years and 9 months after the date GC was granted.
However, it is absolutely impossible to get GC just for 1 year and 3 months after entry (you have to wait 1 year with application, and 3 months is not enough for processing time).
So, there is only a small portion of truth in what you said - that the time starts not from the date of AOS decision. All the rest is not correct.