If that were truly the case, the logical route of it instead locking onto the closest high powers of Yajirobe, Chichi and Gyumao would be what happened.
Right after checking Tenshinhan and Yamcha with the scouter, Bulma stated that it can also spot people all over the world. She doesn't need to read Yajirobe or Chaozu to prover this point, considering she also said it spots powerful people all over the world, so spoting the most powerful people besides the ones that were there makes sense. They'd be wishing to locate the other powerful warriors, so that was the way of showing they could do it with this nw device. Tenshinhan doesn't need to be at full power there.
Goku had no idea Piccolo had trained with weighted clothing, nor that he was suppressing his power. Whatever level 23rd TB Piccolo's power is battle power-wise, it'd be below BoZ Piccolo's level of 322.
Not really. Goku just showed surprise at the fact that Piccolo had been training armored, but that in no way implies weighted Piccolo was below his 23rd Budokai self. Even if Piccolo were putting out power below his ful ppwer 23rd self, the surprise coming from Piccolo fighting armored could still raise in Goku's head as Goku couldn't fully access Piccolo's power until he fought with him in the 23rd Budokai. He just commented on Piccolo's power when this latter showed a glimpse of his power in the prelims. So this proves nothing.
In other words, placing secondary sources over primary sources.
No, because the numbers from beginning of Z were still given in the manga, so they are still a manga's source. If they contradict what was shown in the manga you can either a) ignore them or b) think those lines in part 1 which denoted a huge power difference (many times stronger and such) were hyperboles or not fully in line with a "many times stronger" increase via a scouter increase.
Choosing b isn't placing the secondary source above the primary one.
Whilst that may be the case, that'd also make trying to correlate battle powers and Part 1 power chains impossibly to concisely measure if you were to throw in such variables, making this entire debate about the validity of these guidebook levels pointless.
The debate would be about how Oozaru Goku (from Beginning of DB) compares to 22nd Budokai Kuririn, and since Tsuru has an offcial battle power of 120 and the aforementioned Oozaru Goku has one of 100, I have no reasons to contest the former's superiority. The Daizenshuu's numbers might have some errors depending of your interpretations, but that's in no way a reason to write the off in this specific reason, as here there's nothing exactly going against them.
That would still imply that Roshi can in some way do something to BoZ Yamcha or Chaozu, when Roshi concedes he's in no way able to keep up with even the latter by the time of the 23rd TB.
Roshi states he is no longer any match for those guys, but that in no way necessarily implies his concentrated attack shoudln't be able to do anything to them. If he is below to them battle power wise, and the other ones have powerful attacks comparable with the KHH, then it stands a reason he'd be no match for them.
We know that Rshi is 139 at the BoZ and that Yamcha is 177 and Chaozu probably below that. So, the gap between Rshin and them is somewhat limited by the own manga's numbers. And it does justice to what Roshi said -- "I am no match for you guys anymore" -- "He was shown to be considerably below them".
Nothing directly proves this beyond assumption. Whilst it's later contradicted by the time of the finals, Piccolo viewed that his goal of world domination would be harder than he thought would suggest Kuririn is at least relevant to Daimao tier.
The one which actually contradicts what was shown (Piccolo and Goku)
There's no assumption. Kuririn stated that both (Goku and Tenshinhan) weren't normal when going by their showcased speed, and Yamcha was surprised by the fact that Tenshinhan considered Goku slow. Since they were only watching their fight and not feeling their blows, what they'd be left to analyze would be their speed. So if a speed akin to young Piccolo Daimao is already out of normal for them, so much so Yamcha doesn't even understand how Tenshinhan can label that as "slow", then they are significantly below that level. That much is shown. So, if Kuririn could match the initial level Piccolo used to fight him, then it's to be expected that the level he used to fight the scrubs in the Budokai wouldn't be above the level his father used to battle Goku three years ago, based on what was said above.
Piccolo saying that after fighting Kuririn doesn't mean much either. I take that to mean "if a guy like this one has already this much strength, then imagine the ones worth a shit [Goku and maybe Tenshinhan]".
Which can't work beyond adding maybe another 10 points or so based on 322 > 23rd TB Piccolo >> Kami >>> 23rd TB Tenshinhan > Prime Piccolo Daimao.
Which can work considering BoZ weighted Piccolo doesn't have to be above his 23rd Budokai full power level.
The very contradictions of these Part 1 numbers (especially the Daimao, Kami, Popo idiocy) puts practically every Part 1 number as debatable. Comparitive feats and statements as evidence are of far greater value than what are overall just a set of numbers with little to no thought put into them. It doesn't make your reasoning wrong, but it doesn't make it directly right either.
The contradiction should make that used number wrong, not ALL numbers listed into the guidebook, specially when this "Tenshinhan vs Piccolo Daimao" doesn't even have to be taken as a contradiction if one assumes Tenshinhan wasn't at full power when read by the scouter, which is also possible considering he also saw how casual Goku was when fighting King Chappa to the point his chi couldn't even be sensed. But maybe if that was a contradiction (it doesn't have to be), then the ones I am arguing about doesn't necessarily have to be ones. An error made in one part of the guidebooks doesn't automatically turns everything else said wrong... maybe more questionable, but not wrong.