2 runners on third base

[strike4]

Watching a game and had a parent ask me about a play. I hope I told him correctly.

R1 on third, R2 on second, two outs, ball hit to F8 who is playing up. F8 throws to F2. R1 goes back to third where R2 is on third base. Both R1 and R2 are standing on third. F2 throws to F5. F5 tags R1. F5 rolls ball to circle and leaves the field thinking it was the third out. R1 runs home and scores winning run.

Parent ask why R1 was not out at third. My answer was that only R2 could be tag out if both were on base at the same time. I based my answer on the fact that both runners could not occupy the same base without risk of one being put out. R1 could not pass R2 and go to second but R2 could attempt to return to second.

Was I right in my explaination?