Yes you can kill someone with the Death Note, without actually possessing one.
That specific rule was probably referring to the Ray Penber accident. What they mean is that despite Ray Penber not possessing a Death Note himself, he could still manipulate his colleagues through the Death Note by filling in the names in the blanks.
The second rule should be read in combination with the first (see below), saying that the effects of the first part of the rule would not only take affect when the owner writes the names in the blanks, but also when some other person does so.
I think you might have been confused on the words "possessing a Death Note", which is more than just "holding a Death Note", I suppose.
- You may also write the cause and/or details of death prior to filling in the name of the individual. Be sure to insert the name in front of the written cause of death. You have about 19 days according to the human calendar in order to fill in a name.
- Even if you do not actually possess the Death Note, the effect will be the same if you can recognize the person and his/her name to place in the blank.