When I meet a new client for an assessment, I have already talked to them and thereby have determined whether I will require a physician’s approval. Even if it appears in the conversation that it may not be necessary, I tell people that I may require it after all if anything comes up during the assessment.
For the assessment itself, I have a whole ‘laundry list’ of items that I like to determine and assess. What I always do is taking pictures against a grid, take a video for a gait analysis, take blood pressure and use the Futrex for determining body composition. But even here are already the first modification: if I deal with very overweight clients, they may not be comfortable having their picture taken. I may also forego the body composition because at high levels of obesity it can be inaccurate. There is a piont when it does not add much to my knowledge and only makes a new client feel uncomfortable.
So to summarize my answer: it depends.
As for other assessments: I decide on the spot which to do or not. My rule is to err on the side of safety. I cannot remember the last time I had somebody do push-ups for 30 seconds.
On the other hand: I like to compile as many ‘tangible’ data as possible so that I (and – more importantly – the client) can see measurable progress.