It would depend on the brand of tyre. You've linked to a generic compatabilty calculator. I'd double check with the Michelin techos because databases are wrong all the time but for a 235/40r18 PS3 the rim range appears to be 8-9.5.
Michelin*Pilot Sport 3
Other brands in the same size might allow a 7.5" fitment. It depends on what case they are using. At Goodyear, the 215/70r14 was made from the same case as a 205/70r14 with more rubber on it. 215/70r14 was low volume size so it saved some money and they could sneak in a small production run without doing heaps of tooling changes. When built it was right at the minimum dimensions for that size. The equivalent Bridgestone was noticeably bigger.
Yokohama were always a small case too and a lot of their tyres were factory approved for a smaller width rim.
A good tyre place will know which brands have a small case & will fit IAW the manufacturers recomendations.
edit: I'm not saying don't do it but I think people should know all the facts before making a decision.
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