It's absolutely right that the person who's just given birth gets to decide who she can cope with as a visitor and when.
But that doesn't mean that a MIL or FIL's hope to see a dgc as soon as possible (even if only briefly) is fundamentally unreasonable in itself.
It's a perfectly natural thing to want. Whether you get it or not is going to depend so much on individual circumstances that there simply isn't a one size fits all rule as whether you should get it.
What's depressing about these threads isn't people saying that the DIL should get to keep the MIL more at arms length than her mum - it is natural for her to want that straight after the birth, and right for her to get it if that's what she wants at that time.
What's depressing is the retro-fitting of actual unreasonableness to the parents in law who want to visit, based on the fact that the DIL (reasonably) gets to decide who she sees.
People seem to be working back from the reasonableness of the DIL getting the final say, to conclude that any visit she blocks must by definition have been an unreasonable demand and oh look, is another example of just how crap MILs can be.
The whole point surely is that as the person who's just given birth you get the final say regardless of how reasonable it is for the person to want to visit, so there's absolutely no need to demonise MILs or any other kind of wannabe visitor or prove that they're unreasonable before exercising that right to the final say.
I do think for what it's worth that that right to the final say should still be exercised with some caution and consideration. If I'd waited until I felt comfortable and relaxed seeing my MIL, she might easily not have seen her gc for years. At some point you have to get over that discomfort and just let the visiting happen - that's when all the stuff about it being her gc too, and the dh's child too, become relevant, and where I'm pretty sure some MILs may get unfairly excluded for a bit longer than is strictly necessary. Whether that point is two days in or two weeks is going to depend so much on individual circumstances that you simply can't give a one size fits all rule for it.