Near the top the seat tube may have been either pinched, ovalized or flared out by past post fitting attempts. The size that counts is the one inside and a little deeper past where the seat tube is split to allow for clamping. How you'll measure down in there to an adequite tolerance will depend on what sort of tools you have available.

Now if you can see that the upper split portion where the post clamps in is clearly squeezed in then you can ease it out slightly and then try your seat post. But if it only gets in partway and sticks before it goes past the point where the seat tube is split then your post is clearly too big and you'll need to get a smaller one. The good news at that point is that it should be easier to measure the true size down in the unsplit portion of the frame's seat tube with the top part opened up a little.

Mind you from the sizes you gave I'm thinking that you need a 27.0 post. And yes, that .2 mm DOES make a huge difference.