This appears to be a case of inadvertant misattribution by the Original Poster. Here is the actual text and its context:

[![enter image description here][1]][1]

<sup>*The Cambridge Grammar of the English Language*, Huddleston & Pullum (2002, p. 198)</sup>

As can be seen, Huddleston & Pullum are of course saying that such a sentence is perfectly fine. However, they note that we're unlikely to see this kind of sentence with *may* in a formal academic text. Although *may* is more formal than *can* here, *get in* is a rather informal idiom, and this particular example would be ambiguous with *may*, because it would likely  be interpreted as conveying epistemic instead of dynamic modality.

To see the difference between dynamic and epistemic meanings consider @Edwin Ashworth's  examples (one of which modified):

 - **Epistemic**: *I don't like the look of that roof! Water may/might get in.* [epistemic deduction]
 - **Dynamic**: *The permeability of the membrane is intentional: oxygen may get in. Carbon dioxide may get in. Water may get in.* [engineered dynamic possibility]

Notice that the text says absolutely nothing about deontic modality (i.e. any ideas about *permission* or anything like that).


  [1]: https://i.sstatic.net/FBAzw.png