Appeal play - how to call it

[DTQ_Blue]

I was PU. R1 on 2nd, 1 out. Batter grounds out F3 unassisted. R1 chugs into 3rd and rounds the base. However she thought there were 3 outs and turned around and began running to her defensive position (thinking someone would bring her glove, I guess) she then realized that there were only 2 outs and would up safe back on 2nd. However she never retouched 3rd on her way. The defensive coach comes out to me and says that R1 missed third on her way back. I turn around and call her out for not retouching, but didn't verbalize that I was making the call "on appeal." My partner says to the whole stadium that the runner is not out and simply surrendered her right to third. I told my partner that that runner was my responsibility once she rounded third and my call would stand. So we talked about this after the game and he told me that unless I verbalized that my call was on appeal, he could only assume that I was making a call I could not make (because that call can only be made on appeal) and even if R1 hadn't retouched 3rd, the correct call is to treat her action as a legal surrender of 3B. So was my call improperly made and was BU correct in his action?