what is the call?

[JLMatthew]

This was in a game I was watching, not calling, and I've never seen it before. HS varsity game under FED rules.

R1 and R2, 1 out. Batter smokes a deep line drive to left center. Center fielder makes a great play and cathes the ball for out two. R2 tags and goes to third. R1 is heading back to 1st base. BR thinks he burned the outfielders and was running hard the whole time going for a double. R1 is on the inside and the BR makes a wide turn, not seeing his teammate R1 or the catch and heads for second. Relay comes to F6 who turns and fires and throws out BR. BU doesn't realize and calls out BR.

Offensive coach comes comes out saying (correctly) that you can't be out twice. Defensive coach wants interference because F6 could've gone backdoor to get R2 at third but was confused thinking BR was actually R1 tagging up and going for second. What's the call?

Thankfully, I got to talk to PU after the game as I work lots and lots of basketball with him. They determined that all the runners were at their bases and there was no chance for a put-out by F6. Because no runners advanced past where they would've been, there was no interference called and the game continued under protest.

Was the call right? Is this a valid protest if the umpires were wrong?