Earlier ones in particular, but thats age as much as anything. However, the beauty of rust is that it's readily apparent to anyone prepared to actually look - if a car rusty then move on and buy one that isnt.
MX 5s do need to be checked, even up to the one Accy is looking at, and they hide their rust until they don't, iyswim. Key area is the leading edge of the rear wheelarch. What has historically happened is that the drains are not kept clear (actually a very easy task once you know where they are) and water finds its way into the sills,* which start to rot. So any bubbling or unevenness in that area is walkaway and don't look back. That said, it's absolutely fixable, even if it happens and all the mechanicals are bombproof and cheap.
*You can actually hear sloshing as you drive!