Marko has knowledge, the PTs at my gym most look like they just did a quick course and are on their merry way.
"look like" - again, you don't know, you're just going on their looks.
When i first joined the 30 mins was not enough. I came straight in and they got me doing all sorts of stuff, no warm up no stretching NOTHING, did not tell me to do so prior either.
When judging others' knowledge, be sure that you are judging from the basis of your own knowledge. If you don't know stuff or your ideas are wrong, your assessment of others' knowledge will be dubious at best. Put another way, you are wrong about warmups and stretching.
There are two kinds of warmup, general and specific. A general warmup is "ten minutes on the treadmill" or the like. A specific warmup is simply doing a slower or lighter version of your work, for example squatting the 20kg bar, then 40kg, then 60kg, then 80kg, before your work squats of 100kg. You can do one or the other, for strength work the specific warmup is usually better. Warmups enhance performance. If you've done 10 minutes of jogging you will be ready to go harder in a conditioning session, if you've lifted 20, then 40, then 60, then 80kg, then the 100kg is going to be easier and you'll get more reps than if you just walked in and tried to lift 100kg cold.
When I work with formerly sedentary beginners I have them do a warmup, but not because I really care if they're warmed up, it's just a way to get them to do some extra work on their cardio fitness. If I tell them, "do 10 minutes of cardio, it's good for you," they usually won't do it. If I say, "do a 10 minute warmup before our session," they usually will. While a warmup won't help their performance much - if you can only do 3 knee pushups and half a bodyweight squat, whether you were on the treadmill for 10 minutes first won't make any difference - it won't do them harm, and as I said will contribute to their cardio fitness.
Stretching after a warmup is only useful if you are going to do flexibility work. Stretching before a strength session will lower your performance and will not reduce the chances of injury, it will have no effect on a cardio or conditioning session. The exception is if you have a particular injury or condition which needs to be dealt with, for example foam rolling the ITB. But a general stretch isn't helpful for strength or cardio/conditioning work.