I have decided that in giving D&D 5E an honest go for a full year -- meaning, I will endeavor to run it consistently over the next year in an attempt to find out if it is The D&D For Me -- and one of the "rules" I made up for myself was that I would not house rule anything. I want to play that game as designed (not "as written" mind you; sometimes errata is a good thing) but then it occurred to me: it is impossible for me to run a game, especially D&D, without creating traps and monsters and items and spells and so on. So, are those kinds of GM creations "house rules" -- or, more to the point, do they serve the same purpose as house rules in that they eschew the published/designed for the GM's preference, therefore not really letting the GM and players engage the system as designed?
There won't be a single opinion on this. I've met players that feel that adding, subtracting, or changing anything the published content constitutes a house rule. There was a 1e player I met that rebelled when he discovered that the DM had used a monster with higher HD than was firmly established by the rules in the MM (at least in his opinion). Thus I was gratified to see that the 3e MM gave HD in a range and established that you didn't need to have the authority of Gygax in order to create variant monsters. I would have assumed the authority whether the rules explicitly granted it or not, but even the opinion, "The DM has the right to change the rules" is not one you'll get agreement on. There are multiple posters on the boards that feel I have no right to call the game I play D&D because I've modified it too much, despite the fact that I could put a character sheet for a 6th level thief or a 3rd level wizard in front of them and it would take them a while to find the differences. Pretty much anyone would instantly recognize it as D&D before they noticed the house rules. I've got a 500+ page house rule document, but the game is no more modified and perhaps less than it might be had I simply selected some combination of the many published variant rules and optional content and compiled that in a single document.
Personally I'm of the opinion that no table has anything but house rules it's just that most of them aren't aware of it. Mostly these rules consist of references to the written rules and small exceptions that they introduce to those rules either intentionally, or because they misread the rules, or because they don't know the rules, or because they think that the rules shouldn't apply in certain situations. For the most part, the groups aren't even aware that they have house rules regarding the subject. Often there are exceptions and assumptions of play that just are never even thought about. An example of a really common house rule might be, "Nothing in this section should be construed to govern the interactions between two NPCs. NPCs when they are not interacting with PCs obey narrative combat rules subject to the DMs interpretation of what is appropriate for the genera."
Fundamentally, I don't believe that there is any real difference between a ruling - that is a judgment that a GM makes regarding how to apply the rules in a situation where the rules are (in his opinion) ambiguous - and a written rule. Once a ruling has been made, it generally begins to carry all the force of a rule only its not written down. Any GM that runs a reasonably complex and mature campaign is going to add dozens of new rulings to the house rules of the game every session. A recent example in my case might be, "What sort of dice throws are involved in leaning off a galloping horse, grab the reins of a runaway coach, and bring it to a halt?" I can think of all sorts of different degrees of complexity that are potentially involved there and all sorts of dice you might call for in different sequences. I doubt that without some prior discussion, any two DMs would run it exactly the same. But once you ran the situation in one particular way, the tendency will be for you to treat all similar situations as variations on the theme.
The only way you ever notice the house rules in most cases is if you play at multiple tables with different conventions of play.
So yes, for my part, I feel you are absolutely right. There is no way to play an RPG without house rules at all. Even if you resolved never to use any homebrew content like custom traps, monsters, or magic items, you'd eventually find yourself in a situation you didn't feel was covered by the rules and then what? You'll find RPG players that hold the opinion that there are no propositions not covered by the rules (because the rules are theoretically universal) or that if a proposition can't be covered by the rules then its invalid and should not be allowed. But I personally believe that they are being rather naïve as well as hidebound. Even as much as the claim that the rules don't cover this situation and therefore the players aren't allowed to try to attempt the proposition is a claim not found in the rules.