That's correct.
Setting expose_php = Off
just prevents the webserver from sending back the X-Powered-By
header.
While one could say that potential hackers could look for out of date versions of PHP with security holes to exploit, they could potentially do the same even if the header was turned off. In my opinion, it is a good thing to do, but do not expect it to offer much protection.
In terms of interacting with third party services, they should not have to care about which version of PHP you are using. They should be able to serve content in platform-agnostic formats such as JSON, XML, etc, so that the services can be consumed by any platform and not just PHP.
In anycase, for them to rely on the "consumer's" PHP version is useless, as the header can be easily turned off and perhaps even manipulated by the server administrator.
Therefore, it shouldn't be a problem turning it off.
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