Telomeres and DNA replication

After the first division of a particular cell, both daughter cells will contain DNA with one parent strand and one daughter strand
5'_________3'(parent strand - complete telomere)
3'_________5'(daughter stand)

The daughter stand is shorter owing to lost telomeres.

I have discoerved, from private research, that telomere binding proteins prevent exonucleases degrading the sticky ends of the parent strand. As such when the second generation of cells divides the third generation will have 2 (out of a total of 8) cells with the same composition as the first generation - i.e:
5'_________3'(parent strand - complete telomere)
3'_________5'(daughter stand)

This will continue in each generation, although the fraction of cells in each generation with this composition will gradually decrease.
Essentially, cell division will result in an immortal line of cells as their telomeres do not shorten more than once (the only shortening happens in the first generation - the next generations, assuming the cell inhertis the 100% stand, will be identical)

My QUESITON IS, have I misunderstood something or is the above description valid?