Lets put it this way. Krillin launched ki blasts that could only physically push Goku back after he caught him off guard. At no point did Goku take any damage in this fight in his base form. And Krillin was only able to do this with strategy. Is Krillin a better martial artist than Frieza? There is a very strong case for that. But There is no way in hell that Krillin could do enough damage to actually win in a battle to the death.
You guys are pretty much saying Krillin > Gohan because he can fight better in tournament rules or Batman > Superman Because he knows better martial arts.
Canonically Krillin is still much weaker than 18. 18 is weaker than base Goku by a lot. TO say otherwise is laughable. So to say that Krillin FORCED Goku to turn super saiyan is pure idiocy. So could the real possibility be, and hear me out, that Goku was doing what he went there to do and was testing Krillin's ability to fight stronger opponents. Because we all know flat out that base Goku could one shot Krillin without a thought.
But God forbid Goku would hold back against an opponent. I mean he's never done that before.
Everything you've said is undermined by the fact that Goku had been actively trying to attack Krillin while in base but was simply and utterly unable to do so. Hence him being overwhelmed. Whether you want to dismiss his feat as simply strategy (which is not the case, given that we know these guys are able to no-sell attacks from people significantly weaker, as shown during Perfect Cell vs Vegeta) is irrelevant; Namek Frieza has no special traits or abilities that would've enabled him to do anything Goku did not do in that skirmish.
In a fight to the death, Krillin would even be more effective given the kiezan / destructo disc and the theoretically broken combo that adding the tayoken / solar flare would involve.
Based on? No really, is there anything besides "there's no way Krillin can be that strong!!!" that makes you think that? Excessive reliance on headcanon is a real issue in this fandom.
Quantifiably speaking, how do tournament rules make Krillin better able to push base Goku back or enable him to even last one second in a beam struggle with SSJB Goku?
Says very little actually. If the writers want 18 to suddenly be a match for base Goku, she will be a match for base Goku. If the writers want her to somehow be able to deflect Goku's kamehameha, she will deflect his kamehameha. Headcanon means nothing. What we see on screen means everything. Hell, they could make Chaotzu > Whis tomorrow and wouldn't be a damn thing we could do about it.
The real possibility is that Krillin (and even Roshi) is a popular character and there needed to be grounds for him to partake in the upcoming tournament arc. Hence, Goku succumbing to the worf effect
Now if the writers change their mind down the road (as Toriyama did in the Buu by having Goku go from telling Piccolo that he gave his all against Fat Buu to telling Vegeta that he held back), it'll be a different story. For time being though, power level headcanon is worthless. Krillin, Roshi, #17, Piccolo and Gohan are strong now. Get used to it.