I found out my fiancé was in rear ended an auto accident about 9 months ago. Neither party called the police but exchanged info. Neither did she report it to her insurance company.
The driver made and signed a written statement that she was at fault. The only damage was to the other party's vehicle. My fiancé went to the ER a day later due to pain throughout her body which has continued to the present. To make a long story short the insurance company offered her a $5200.00 settlement of which $4900.00 she is suppose to pay for the medical treatments she received.

Since there was no police report but a signed statement by the driver as to being at fault. If she has to be taken to court, is the statement as valid as a police report due to her admitting being at fault?

Why would she have to pay the medical bills when she wasn't at fault and the other driver is fully insured?

What State? In some States the company won't pay anything unless the claim is filed within a certain number of days. I see she got medical treatment but can't determine if the accident was reported.

A Police Report (unless the Officer actually witnessed the accident) is pretty much hearsay, very often discredited. That's what investigators do (by the way). A written, signed statement admitting fault is admissible and pretty much ends the argument about fault.

It is entirely possible that the insurance company will not pay for pain and suffering and medical bills unless she has an Attorney. The company is going to continue to come in with low figures.

I see a lot of accidents where pain and suffering are not paid because there either is no medical documentation that there WAS pain/suffering, no time was missed from work, many factors.

... the insurance company offered her a $5200.00 settlement of which $4900.00 she is suppose to pay for the medical treatments she received.
...
Why would she have to pay the medical bills when she wasn't at fault and the other driver is fully insured?

$5,200 less $4,900 leaves $300, if my math is correct. If she were to accept this offer she would have her medical bills paid and an extra $300. You say that her vehicle wasn't damaged so, assuming there is no lingering medical issues, the $300 goes to pain and suffering and she is made whole. What do you mean "she [would] have to pay the medical bills"?