There is no one true way to play D&D. Personally, I consider this the soul of "Old School" D&D. You bought the rules (be they Original D&D, AD&D, B/X D&D, or BECMI D&D) and you as GM get to do with them whatever you want. The rules are just guidelines for creating your unique campaign. If you want to base your game on OD&D but take what you like from AD&D, the Arduin Grimoires, Gamma World, Runequest, and a bunch of stuff from Dragon, White Dwarf, and Different Worlds and mix that with a heaping helping of your own house rules and call the result "playing D&D" that's fine. This is how campaigns worked in the 1970s and early 1980s. Very few people gave a damn about official rules and exactly what version of D&D was being played.
Some players who played D&D in the 1970s seem to have forgotten this and have developed a "rules purism" that would make many a "new school" player proud. I'm not sure where the "rules-purism" I see among some grognards today comes from. It was a (very tiny) minority position in the 1970s, IMHO. They seem to have forgotten how little people cared back when "old school" was the bright and shiny new game on the block.
Most people played OD&D with thieves (and most of the other classes from Greyhawk). Really, they did. But games that didn't have them weren't considered not really D&D. People modified the combat system all the time. This is why the argument over ascending/descending AC in grognard circles today strikes me as silly. I saw OD&D (and AD&D and other TSR D&Ds) played with all sorts of modified to-hit tables: ascending, descending, percentage, attribute-based, playing card based(!!), etc. My favorite weird one was probably the one a friend used where hit points remaining were used instead of levels in the to-hit table (so the more "wounded/tired" a being was, the less accurately they hit).
Yet I've gotten lectured in email on the evils of some of the optional rules for m74 I put in Ancients Aurguries and my post on Body Points and Hit Points for S&W -- claiming that such optional rules are "too far" from OD&D. This despite the fact that I was using an earlier form of the BP/HP split as early as 1977 or so. I haven't published the "spell point" part of my BP/HP system because I'm not in the mood to deal with the fallout. Spell points are evil, you know, and make OD&D not OD&D even though adding some type of spell point system was a very early and relatively common house rule for OD&D. ::sigh::
At times, I feel like I've walked into some alternate timeline where the various editions of TSR D&D were played very strictly by the book in the 1970s and 1980s, where the various TSR editions of D&D were so different that adventures written for one edition simply could not be used in any of the others without the DM spending days rewriting them, and where house rules that changed whatever someone thought were the core of D&D resulted in the offending DM being jailed. That's just not the reality I gamed in.
If you are telling others that they can't do x or use rule y in their D&D game and still be "old school" -- especially if things like x and y were done in some "D&D" campaigns back in the 1974-1984 era -- I have to question just how old school you really are. Sure, it is possible to drift into "new school" if you aren't careful but "old school D&D" can stand many more changes than many grognards seem willing to tolerate today.
Note: Since I wrote the first draft of this rant this morning, I discovered a post Dave at Sham's Grog 'n Blog made today: It's all D&D to me. This post makes a similar point. We called what we played "D&D" back in the day no matter how many different editions of D&D we borrowed ideas and rules from.