I'm surprised (still) that people are shocked by being asked to write your own recommendation. This is EXTREMELY common in the workforce. Depending on how big your company is, your boss usually don't know you on such a level to write a top notch recommendation. For instance, I used to supervise and write performance reports on 30 people. Of course I knew them all, but I could never keep track of every important thing that each of them did. It would be a disservice to them to not ask for their input to a performance evaluation and for them to highlight their best work (ie similar to a recommendation). YOU are your own best advocate. I promise that many of these so called "good" recommendations that you think the person is writing for you are mostly form recommendations that say the same thing over and over. When you ask for a recommendation, be up front that you will provide a bulleted list of your accomplishments (not all of them, don't overwhelm them). Also for an open format letter like in PTCAS where they can write what they want, I suggest giving your writer some areas to focus on. "Could you focus on my ability to handle a stressful schedule, or my ability to work with patients, or my initiative.....and here are some ways that I directly demonstrated those things to you X, Y, Z". The PT you shadowed for cannot remember every instance and they will be grateful you kept a log and provided it to them at recommendation time.
In many cases, you won't develop a true personal relationship with the PT and that's OK. The goal is a professional one. It's OK if you don't have a million observation hours, many schools only require 50 or so. If you did those 50 hours at even 2 different locations, that's not a lot of contact time with a PT. But....if you go with bulleted list and some ideas for the PT, it gives them much more to write about and you will get a stronger reference in the end. Sell yourself!!! Gosh knows you will be asked to do it again at interview time. Be grateful for those people who ask you to write your own reference. This is a great skill you will carry with you for life....and a huge plus to your application.
(**Just to be clear as I feel there are some misunderstandings in this thread. When someone says "yes, I will give you a recommendation but please write your own", you aren't actually logging into PTCAS as them and typing it in. You basically write a draft copy and submit it to the recommender. The recommender may or may not edit the draft, in fact the final version may look very different. Or it won't at all. But by the recommender reviewing it, putting it in PTCAS and signing it, they are acknowledging that is their evaluation of you. Again, VERY common in the professional setting for anything from speech writing, to performance evaluations, to position papers, to company wide emails sent out by the boss.)