There is no rules support for this interpretation
Nothing in any 5E rules I'm aware of limits Warlock or Sorcerer items to specific subclasses of those classes (there may be individual specific items that do this, but simply being tied to the Warlock/Sorcerer class would not).
There is no guarantee that any but the most common magic items (e.g. potions of healing) are available for sale, so your DM is well within their rights to deny purchasing items, by any class, but claiming Warlock-specific items must be gifted by the Patron is inventing rules; there's no meaningful rules support for this sort of restriction, and it's a nerf to the class if they're simply not eligible to get basic power-boosting items for their class (e.g. Rod of the Pact Keeper) where other classes can get their equivalents without strings.
I can't see much of an argument for applying this rule to Warlocks that wouldn't equally apply to Clerics (not just on domain subclass, but on patron deity). If a Warlock can't use Warlock-specific items created by Warlocks of other Patrons, it should be equally impossible for a Cleric of Selûne to use a Cleric-specific item created by a Cleric of Shar, and vice versa.