It is not legit. Who said that those holding immediately before shmoneh esrei cannot say amen? In fact the Rama holds you SHOULD say amen… “v’chain nohagim”.
It is the Mechaber who says it is assur to answer amen at that point, but Ashkenazim generally follow the psak of the Rama.
The minhug evolved not to answer amen in spite of the Rama’s psak, and the Mishna Brura’s solution (to accomodate both the Mechaber and the Rama) is to say tzur yisrael together with the shliach tzibbur being that one does not say amen to his own bracha.
No one suggests that the shliach tzibbur should say it quietly. As I wrote earlier this is purely a minhag ta’us.