I'm not sure if they would or not. I'm sure they employ security researchers. What I don't know is, if Intel was the first to discover a vulnerability of this size and knew that mitigation would impact performance, whether they would have tried to cover it up. I expect that they would have disclosed the vulnerability as soon as they had a mitigation option.
But Intel wasn't the first to discover the Spectre (and Meltdown), and therefore they were stuck with the disadvantage of having to respond to outsiders discovering a vulnerability, rather than being able to get out in front of it, which is what AMD is doing right now. The end result is the same with both brands: you have to disable speculative execution and take a hit to secure your computer, and I don't think either company should be telling customers not to worry. But AMD has the messaging advantage.
But Intel wasn't the first to discover the Spectre (and Meltdown), and therefore they were stuck with the disadvantage of having to respond to outsiders discovering a vulnerability, rather than being able to get out in front of it, which is what AMD is doing right now. The end result is the same with both brands: you have to disable speculative execution and take a hit to secure your computer, and I don't think either company should be telling customers not to worry. But AMD has the messaging advantage.