Sorry cricketballs, but yes!
Ever heard the phrase 'with rights come responsibilities'? 
I think the poster that said that was trying to make the point that it's a bit rich for an expectant father to jump up and start banging on about his 'rights' to influence how the birth is undertaken for HIS peace of mind, and then back out of the room whimpering when the nasty scary old instruments start coming out!
If it's your view that the father - and by extension his mum, because you persist in seeing this issue as one of familial competition despite the OP saying that she wants her MIL not told simply because her MIL is a pain - if it's your view that the father to be is EQUALLY a part of the process, is EQUALLY 'at the centre' of the birth then no, he does not get to be 'not comfortable' with the icky bits - the other parent can't get up off the bed and say 'ooh sorry I'm not up for this bit' - so neither should he!
But a good dad-to-be knows that and simply wouldn't think in a million years of waiting until his wife was undergoing unpleasant bits of the birth process and then decide to pop off for some 'support' from his mum and leave her to it. A good birth partner wouldn't think that his feelings at that point were a priority.
This thread has become about what the OP isn't - familial competition. It's not hard to smell the fear in the posts of the mums of boys here, and I think that that is really sad, and just not necessary. Bottom line - no, it isn't the same knowing that your daughter is giving birth as knowing that your son is watching his wife/partner give birth. The latter doesn't involve the irrational but naked fear that it will be your child who dies during the process or who ends up permanently damaged. Or the agony that you know your child is in pain, perhaps frightened, and there's nothing you can (or should) do about it. Anyone trying to equate the two just makes themselves look desperate and unreasonable.
I find it bizarre that on this thread some people are putting more effort into denying the realities of biology in order to convince themselves that they are an equal grandparent, rather than simply fostering relationships with the next generation - their son and wife, or daughter and husband - which will ensure that they do indeed become as central and as loved as anyone else in the family.
Growing up I do not remember any feeling of one set of grandparents being more involved or central than the other. My mother called her MIL 'mum'. As I could see it, tensions - and there were plenty! - arose not from whose child was whose and whose side someone was on, but just from individual personalities. So, a normal bickering old family, but thank God, one where at least key members hadn't started out from the basic, fatal premise that there were two teams, and everyone was on one of them, apart from the grandchildren, who were to be competed for.
That's the issue I see here. I find it sad that some on here, mums of boys it mainly seems, are taking the trouble to go on about what would hypothetically be 'their' child's rights in this situation. Godammit, can't you see that the one thing that would be most likely to see you pushed out when it comes to your hypothetical future family is taking that attitude, that you are there to fight for YOUR child!
What I applaud are the people who just don't think like this, who see their children's partners as an equal part of the new next generation that they love in their own right. The kind of mothers who become cherished grandmothers are the ones who say 'Sorry, I'm not thinking so much of my son here - it's my darling DIL who's going through the birth!' Or, 'Sorry, I'm not thinking so much of my daughter here - it's my darling SIL who has the broken leg/appendicitis/who is working the 70hour week' (delete as appropriate).
These are the grandparents who have it right. Their attitude supports the next generation, as a family in their own right, rather than working against it at some level. They have the maturity to accept that their own parenthood is now secondary to their child and child-in-law's. They are the grandparents whose name is never a source of conflict in their grandchildren's home. They are the ones who are loved and turned to, and it doesn't matter whose parent they happen to be.
Anyway- all that's seocndary. People, I REPEAT - the OP wants to not tell her MIL because her MIL is a drama queen. Not because she is her MIL and therefore to be vanquished. I think that's sensible. If the OP was saying 'I don't want to tell my sister/my mum/my hairdresser because she's a drama queen', people would be saying fine. It is fine.