I used to store my Gaviscon Advance in the fridge until, like you I read the label after a few years of guzzling down bottles of it, always worked, the reason I kept mine in fridge was because usually most bottles of medicine read, "keep refrigerated once opened".
I have been taking Gaviscon for years.While I don't keep it in the fridge(it's not necessary)my bedroom is unheated and is often (in the Winter)colder than the fridge,and nothing bad has happened to the Gaviscon.It's made(principally) from seaweed,so can't see what fridge temperatures would do to spoil it?
Gaviscon(and similar medicines) contain large amounts of sodium alginate, which make it viscous. I'd guess that the lower the temperature, the thicker it gets...so you can't mix it properly by shaking....and it may get so thick, it becomes difficult to get it out of the bottle.
That's my theory, anyway!