Sorry you had a bad experience.
The Delta lounge finder doesn't list any lounges in HAV. Since you were flying DL their access rules prevail.
http://www.delta.com/skyclub/skyclub...Request.action
Other SkyTeam airlines that serve HAV may have a contractual agreement with the third-party lounge there which would explain the SkyTeam logo. But as you pointed out, the lounge is a third-party lounge and not a SkyTeam lounge (like can be found in LHR, IST, etc.) and therefore each airline would need to provide access.
Originally Posted by
readywhenyouare
I would not have done what you described. Drinks and snack food are not worth it. I wouldn't have done what you did in a place like Cuba. Just my opinion though.
+1 a "thanks for checking, have a nice day" should have been the end of this entire interaction.