Question: Do the rules indicate anywhere that intelligent magic items should, in fact, have no construct racial Hit Dice?
Answer: No, the rules do not indicate anywhere that intelligent magic items should have no construct racial Hit Dice. However, the rules also do not indicate anywhere that intelligent magic items should have construct racial Hit Dice… or any kind of Hit Dice, for that matter. Because of this, by default, intelligent magic items don't have Hit Dice.
This made more sense before the 3.5 revision
Prior to the 3.5 revision, constructs received no feats and no skill points due to Hit Dice, no matter their Intelligence scores. Further, constructs didn't receive extra hit points based on their size. (See the Monster Manual (2000) section Reading the Entries on the Size and Type construct (5) and Creature Advancement by Type on construct (13) or hunt down that information in the section Monster Overview here.)
Combined, this meant that when the Dungeon Master's Guide (2000) said, "Intelligent items can actually be considered creatures since they have Intelligence, Wisdom, and Charisma scores" (228), they could be more easily considered a construct. Even without Hit Dice, they could do what the DMG said they can do—use their powers, possibly communicate, use their hearing and sight to perceive some distance around them, and so on—, all despite possessing Constitution, Dexterity, and Strength as nonabilities and possessing no Hit Dice.
The type construct changed with the 3.5 revision, but the Dungeon Master's Guide section on Intelligent Magic Items only changed superficially (e.g. adding powers, changing prices). This left intelligent magic items in a very weird place, rules-wise: They still weren't wholly creatures that possess the construct type as they possessed no Hit Dice therefore they gained no skills and no feats, yet the game continued to say to consider them creatures, just as it had prior to the 3.5 revision.
(This reader believes a minor attempt was made to reconcile this disparity with the 6th-level Sor/Wiz spell Nybor's psychic imprint [trans] (Magic Books of Faerûn Web column "Nybor's Small Codex: Spells from a Former Zulkir"). That spell allows the caster to stick a creature's personality into a magic item to make an intelligent magic item, and, from then on, the personality is forever unchanging. Seriously, to this reader the spell seems like a 500-word excuse as to why—at least in the Forgotten Realms—intelligent magic items don't have skills and feats by default.)
And this is how things have stayed… all the way through Pathfinder. And, as Pathfinder's first edition approaches a close—over a decade after Wizards of the Coast ceased publication of Dungeons & Dragons 3.5—and seems to be transitioning toward a second edition far removed from its original material, it seems this issue—"Intelligent Magic Items: Are They Constructs and, If So, How Much Are They Constructs?"—will never be adequately addressed by the folks who worked on Dungeons & Dragons, Third Edition. (James Jacobs, I'm looking at you.)