Sentence Correction

Dear All,

Please help explain why we dont have a tense error here :

"After the president of the college publicly lamented the sharp drop in the value of its endowment, the head of faculty suggested that they initiate a fundraising campaign immediately. "

Is corrected by :
" After the president of the college publicly lamented the sharp drop in the value of its endowment, the head of faculty suggested that the college initiate a fundraising campaign immediately. "

I understand the pronoun error. But why isn't there any tense error ?

Shouldn't it be :
" After the president of the college had publicly lamented the sharp drop in the value of its endowment, the head of faculty suggested that the college initiate a fundraising campaign immediately. "

Thanks in advance![/u]