[EDIT] I just caught up with an internal Adobe communication for independents like me, and it's correct. So my earlier answer (below the line) was not up to date.

I must say, this is the craziest thing I've ever experienced with their business, but my NDA prevents me from knowing/telling anything more about its backgrounds.

You're officially licensed to download and use the current version and/or the version before that (e.g. the current CC 2019 and its predecessor CC 2018).

Older versions will still work, but they won't be able for download anymore and Adobe needs to warn you that you might get sued if you still use them.

This policy is due from the 10th of May, and there are no exceptions.

The much older, perpetually licensed and registered CS versions are not affected.

This is a helpful page: Adobe Limits Software Version Downloads

Official Adobe blog: Changes to Creative Cloud Download Availability

[Earlier and incorrect answer]

This is absolutely not true. Adobe is not telling such things.
Who ever is spreading this story, is telling nonsense.

Oorspronkelijk geplaatst op Quora: Why would Adobe tell users they can get sued for using old versions of Photoshop? Is Adobe telling the truth when they say this?"