Let me see if I understand your argument. It looks like it's based on three premises with two conclusions:
1) Premise: The Senzu do not have wards that good (therefore private SSJ-capable training rooms cannot exist)
2) Premise: A house that secret trained SSJ did so in the Training Hall (therefore private SSJ-capable training rooms do not exist)
3) Premise: Only the Training Hall has wards that can hide a SSJ (therefore we'd know if she were training herself up)
4) Conclusion: Because of (1) and (2), Dandeer cannot construct her own SSJ-capable training room.
5) Conclusion: Therefore, because of (3), Dandeer cannot become a super-saiyan, nor train up her SSJ powers, in secret.
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(1) does not support (4) because the Senzu have good reasons to not try to have an SSJ-capable training room. If they ever did, they would have been forced by Yammar to de-ward their room after the Talt rebellion and start over with something that would pop like a soap bubble under SSJ power levels, like what they now have. Even now, they have taken pains NOT to go super-saiyan despite years of formally being in rebellion, precisely because they do not want to commit that unforgivable offense. (1) is at best weak evidence for (4), because there is little or no evidence that the Senzu WANT wards that good, when the very existence of wards that good would be evidence of intent to rebel.
(2) does not support (4) well, because it is unclear how much sorcerous support the Talts had in their rebellion. Now, it would clearly take top-flight sorcery support to create an SSJ-capable training room, even assuming if this can be done at all[/i]. The Talts may simply not have had the resources to accomplish this thing.
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With (4) being at best poorly supported by a mix of circumstantial and weak evidence, (3) stops being a matter of "fact that we know" and becomes "my opinion." This opinion may very well be true, but it's not certain to be true, and should not be treated as grounds to just completely ignore the entire question.
And since (3) is far from certain, conclusion (5), the important one, falls apart. We can say that Dandeer probably doesn't plan on becoming a super-saiyan in secret and probably can't do so, but we can't say she definitely can't do so in the sense that she cannot perform other extraordinary feats (say, growing Senzu beans on her own, or becoming a Seer).
Now, just to make this extremely clear, I am not asserting that Dandeer does have secret plans to become a super-saiyan and ruin our day in that specific fashion. I am not even asserting that she can accomplish this thing. I am asserting that there are specific, plausible mechanisms, using only known tools and resources that we know Dandeer has, by which she might be able to accomplish this thing.
So for example, we MIIIIGHT maybe kinda sorta want to at least brainstorm a little about how we might test for whether this alarming possibility is or is not a real threat that might actually materialize.
How might we test? What are our assets?
Well, to think a little:
1) Kakara has very possibly the best ki sense on the planet. Is there a way to tell the difference by 'feel' between the ki of a person who has SSJ-level powers but is not using them and has not powered up, versus the ki of a person who lacks such powers?
2) We might be able to quiz Jaffur/Jaron and thus get partial information on Dandeer's movements. Does she conspicuously spend significant amounts of time away from home that are not accounted for by her known, normal activities? Does she show signs of fatigue or other evidence of undergoing heavy power level training?
3) We may be able to scan obvious areas where Dandeer might hypothetically hide a small warded training room (such as under her own house), although I'm pretty sure we couldn't scan all of Garenhuld in this way, so we might not be able to find a secret training room if she's put it somewhere out in the wilderness.
4) If we get an opportunity to talk to a friendly sorceror, or for that matter to Berra/Apra/Yammar, we might ask if they know whether or not a sufficiently skilled sorceror could create such a room for themselves, at least in principle.
These would all be relatively easy precautions to take, so we might want to consider one or more of them. (2) in particular might be useful for detecting other entirely different categories of things Dandeer could menace us with, and so might (3).
