If by filing the affidavit you mean that you are submitting it to the CRA as part of your request to block information from your credit report, no, you dont "lose any rights."
To amplify, if you are asserting identity theft and getting the identity theft information blocked from your credit report, you are using the procedure set forth in FCRA 605B
That process requires both a copy of a police report (which the FCRA calls an "identity theft report") along with a statement that you never authroized the transaction at issue.
While an FTC Identit Theft Addidavit is NOT an express requirment of section 605B, one of the CRAs want that affidavit as their means of satisfying the statement requiremnt of section 605B, so it is best to just execute and include it with your request to block.
By submitting the police report and identity theft affidavit to the CRA, you are asserting your right to require the CRA to block the identified identity theft information from your credit report. You are not giving up any rights, you are enforcing your statutory right to exclusion.
