Stephen,
I read once that you can ask 10 different wine makers a question and get back eleven different answers. This is not rocket science, so each of us over a period of time tend to do things by "what has always worked for us".
So, if you go by your kit instructions, using the kit supplied yeast, and it doesn't say anything about snapping or not snapping the lid down during primary, you likely won't have to worry about it, one way or the other
Have you been taking specific gravity readings with a hydrometer?
Here is my own personal experience:
During primary, the yeast need oxygen; during secondary (and thereafter), they need to be kept from oxygen. That is a scientific fact, regardless of the kit instructions. Now that's why I stir during primary.
While in primary, it is not a good idea to seal the wine from any and all oxygen. I believe the foam should be stirred in on a daily basis, better if done twice a day. Also, stirring is especially necessary if you have added a grape pack. If left on top too long, the grape pack can produce mold and/or start rotting.
However, if no grape pack and if you are not getting a lot of foam and your lid is not snapped down (sealed), you should be getting enough circulation to be OK. I say "OK", but I will always stir it anyway.
Being OK is more true if you are using a very robust yeast like EC-1116 or EC-1118 and a few other of the "Mack Truck" yeasts; they are very good at getting the job done correctly, even under not so great conditions, like having the lid sealed during primary. I typically don't use these particular yeasts, which is part of the reason why I got H2S in the past.
Now if you don't practice very good sanitation, you would be better off not opening the wine to stir, but I'll assume you are going to always sanitize your stirring spoon and do it correctly.
My advice - Don't seal the lid during primary, don't leave lid so critters can get into the wine; stir the foam down at least once a day using a well sanitized stirrer... That's one of eleven!