Luridia, I hope you don't take what I'm about to say the wrong way...
"If a puppy growled at me, I’d be really surprised too, so I would have crouched down and held out my hand for it to sniff to try and make contact."
A dog that growls is asking for space. By approaching, you create tension, so you risk escalating a simple growl into a bite. Especially since you’re looking at the dog (quite an aggressive signal) and crouching down (we tend to lean forward when we do this, which a dog sees as a fairly aggressive signal)...
If the dog starts barking after it’s been growling, it’s very likely we’re dealing with a dog trying to push us away because it’s scared. Usually, a bite follows a growl if you keep approaching. If something else happens, it’s because the dog is really trying to get more room... Haï Olly might react that way, even if it’s not necessarily the most logical response.
"Then you have to see how the dog reacts, but if it starts barking, I look stern and say a firm 'no'."
Using "no" is positive punishment—you’re adding something unpleasant or even scary to stop the behaviour. That is the very definition of "no", and it’s a far cry from positive reinforcement training... and a simple "no" can trigger a bite, considering you’re close to a dog that’s asking for distance and you’re adding more pressure.
"I always say 'no' when the dog barks"
When we say "no", we’re paying attention to the dog, looking at it, communicating with it... Many dogs bark to get attention. The "no" then reinforces the behaviour instead of stopping it. It’s counterproductive—it’s a bit like you’re "barking along with it".
"And if it doesn't shut up when I say no, then I say it again and make it lie down by pushing gently on its back and saying 'down'."
Positive punishment + negative reinforcement (pushing them to lie down) is purely coercive training, even if it's relatively gentle. This is the type of training that causes the most bites... When dealing with a dog barking for space, it’s even more dangerous because you’re initiating physical contact. There’s a huge risk it will turn into self-defence, leading to bites.
"And if my dog grabs my trousers and starts tearing them, I get cross. I say 'No' and 'That's enough', and if that doesn't work, I grab it and put it in another room so it calms down."
Getting angry at a dog that’s biting tends to over-excite it and makes the bites harder. Isolating them is a good move in my opinion, but the "no" and the actions before that risk making the situation worse.
I recommend this article about the word "no" (on page 16): http://www.cynopsy.fr/cynopsymag/CynoPsy_Mag_N4.pdf