To address your specific question first... if the owner of the other dog thinks it isn't a good idea then it definitely isn't a good idea. It is very important to have dog socialization but they must be appropriate interactions. If the owner feels uncomfortable with the situation their dog will read into that and may also become uncomfortable. When you are thinking of letting your dog meet another dog take a look at the owner. If they don't seem relaxed, if they are holding the leash tightly, or if they don't have control of their dog then skip it... this isn't the one you want to take the chance on. If both the person and the dog seem relaxed, the dog is not pulling on the end of the leash to get to you, and the person says it is OK then it could be fine.
For the leash part of the question, there are many dogs that are leash aggressive so the concern the people showed may be that their dogs have some leash issues. Just because you didn't witness it at that moment doesn't mean that the dogs are always OK. The owners may have been very carefully managing the situation and you might not have even noticed. So, if they are worried... respect that and don't try to force the meeting. I noticed that you say "if they start fighting the leash could be a great help", that makes me think that you've had a couple experiences where you had leash fights. I would really encourage you to do a little more reading and watching some video's on dog body language... usually you can see a dog fight before it happens. Sometimes it happens to quickly but that might mean you rushed the evaluation part and didn't allow for enough time to get a real read on the dogs.
In general a good thing to remember is that you should be much more concerned with the quality of the dogs interactions more than just the frequency of them. One good interaction can be worth 20 so-so interactions and a bad interaction can end up in an injury or a dog that is then scared or aggressive toward other dogs. So if the people are worried then that is unlikely to turn into a great interaction and it's probably not worth the trouble. I know that it is fun to find great playmates for your puppy and, at times, it feels that we NEED them to get rid of energy but you do need to find the right kind of playmates.
There are several different types of puppy experiences that are going to be important.
One is playing with other puppies of similar age and reasonably similar size or play style. These interactions let the puppies practice all kinds of play-bow, meeting, running, wrestling, and bite inhibition that really are best for puppies to learn from each other and are typically pretty safe. Oh , and they get rid of each others puppy energy!
Another is learning how to interact with adult dogs. If you can find an APPROPRIATE adult dog these lessons teach the puppy good dog manners. But not all adult dogs are appropriate with puppies, many adult dogs find them pretty offensive. For instance it is bad manners to run up in another dogs face, lick their face/lips excessively, or be in general pushy the way puppies are. A good adult dog can correct the puppy without hurting them, the puppy will likely pout a little after this but will have learned that if they want to interact with other adult dogs they have to have some self-control and respect other dogs space. A really good adult dog will even play with a puppy but this too is a minority of the adult dogs.
Just as important as those experiences is learning that you don't get to greet every dog and that it isn't the puppies choice who it greets. I really like how the book "Control Unleashed" describes how to teach this. In the book she describes a system for teaching the dog that when they give you the attention instead of the other dog sometimes they are rewarded by getting to go say hi to the other dog. It works as a very nice natural reward system that rewards the dog with what they really want for doing what you really want. It is best if you can set up a time with a friend so that you can have control over when the release to go play happens and you can wait until the puppy gives you attention before they get the reward of play. It doesn't have to be a long drawn out thing... just a quick routine of letting you get the leash of while the puppy is still sitting is a great way to start. You can practice this many times during the play session, just call the puppy back to you and reward it for coming then get a sit, reward the sit, then say "go say hi" and let the puppy go back to playing. The puppy will quickly learn that coming to you is rewarding and that you even let them continue to play.
