We are talking about four great lamas from different lineage now, HH Dalai Lama from Gelug, HH Panchen Lama from Gelug, HH Karmapa Urgyen Trinley and HH Karmapa Thaye Dorje from Karma Kagyu. As far as I understand HH Dalai Lama is the head of politic and spiritual in Tibet from the 5th Dalai Lama time, but even that time, HHDL never involve with the recognition of HH Karmapa because Karma Kagyu have a complete system to recognize their throne holder.
It's quite surprise to see HHDL actually recognize the current HH Karmapa Urgyen Trinley as the reincarnation of HH 16th Karmapa, because it never happened in the hundred of years of Karma Kagyu history. By doing this actually created a big problem for us in the future, let's say if HHDL passed away (thousand years from now) and HH Panchen Lama recognize a 15th HHDL, HH Sakya Trinzin Rinpoche also recognize a new 15th HHDL, and HH Karmapa also recognize another 15th HHDL, which one should we follow ? I understand 3 might also be the emanation of 14th HHDL but who should we stick to ?? It might not be a problem to highly attained lamas, but most of us are just common people who know very little dharma, this will create very unnecessary trouble.
This will also open a can of worms that whoever in the future can just recognize whoever lama as they like, so which will be the real lineage that we suppose to follow ? It's very important for us to know where our lineage come from because, it can created "spiritual war" in between different school of Buddhism.