Lenslay‘s husband was totally astonished by the unexpected visit. "I don't think we would have randomly invited him over but we appreciate it and the gifts." he said.

引号内的句子确实是转移否定句。如果把not还原到从句，则只有一个结果，即：

We wouldn't have randomly invited him over but we appreciate it and the gifts.

这是对过去所做的推测：我们是不会随邀请他来做客的。实际我们也没有邀请他，他不请自来。所以这不是虚拟语气，而是对过去情况所做的推测。