No way. My previous FTO tried this one on people and they believed it. Nowhere is it written in JAR-FCL that you need to clock all hours at your FTO. Be warned, if they're telling porkies like this, what will they try next?!
Your P1 hours can come from anywhere as long as they're true P1 on a rated type. If you're rated, fly it anywhere in the world you can, like 206 in LA for USD135 per hour flying for radio stations!