Hi Edmond
You'd be able to use the copy without any problems, but you won't be able to rank for it specifically. If that's not an issue, then read on.
What I would do is add a canonical tag on your page back to the original press release. You can read up on canonical tags here in this Moz guide.
So say the press release is at this URL: http://www.pressreleasecompany.com/yourpressrelease
You can take the press release and publish it on your own page, such as: http://www.yourdomain.com/yourpressrelease
On your webpage, you would need to have the following code in the section of your HTML:
rel="canonical" href="http://www.pressreleasecompany.com/yourpressrelease" />
With that bit of code, you are letting Google know that you have taken the press release from elsewhere and that the original copy can be found there. You are using the copy just to feature and add user experience to your website, and not to try and rank for any terms.
Google will acknowledge the tag and will not penalise you (or reward you) for using the duplicate copy. I think it's also a good idea to include a brief introduction to where the press release came from and what it is about before using the copy, just to show that you are citing your source.
With those steps, you will be fine in mentioning external press releases about your company on your own site without risking being penalised. Always a good idea not to overdo it, but with the canonical tag you won't be seen as duplicating content for nefarious or ranking means.
Hope this helps.