Yes, the T&C's were clear about the stays needed to be completed on or before June 30th. I don't know if they would have had an issue with back-to-back stays past 6/30. But as we know, some CSR's are not so strict about the rules. You might find a more sympathetic agent if you call and polietly explain you would have done a paid stay instead of a point stay had you realized the stay starting June 30 would NOT count.
Hilton is far from my most favorite chain, but you are not being ripped off, just someone enforcing the letter of the promo. I do believe Hilton was being a bit deceptive as many would have assumed stays through June would have counted. I've started noting the specific start and stop dates for promos as others are getting wierd