I use saiyan beyond god because it's in the wiki but I don't think the name itself makes much of a difference to the discussion. As far as it being a form though, the manga and anime give more than enough context for that. How is it that they are so strong in base form if they are not using some measure of god ki? Going by what berus says, goku in base form before their first fight would not be able to defeat frieza. However a while later goku is able to fight with frieza without using SSB even though first form frieza outclassed SS gohan. So even if the name is not cannon and whatnot, they are clearly doing something to be so insanely powerful in their base forms.
That said, I am not entire sure the implication here is that SSBG is stronger than SSG.
As for the bold part, I don't think that is an issue at all. It would be a similar situation to OP with armor haki for instance. So yeah, we would have to be told in some form or another to know what they are doing in their base forms.
You can't look that Deep into DBS it's too inconsistent in showings. Powerscaling & even cannon showings are Juss inconsistent & in jumbles.
*Here's the thing....Base Goku & Vegeta should hands be strong ASF! SSB shouldn't even be used because they are basically clad in God Ki, so their opponents should be Godly like also.
* Base Goku is the only character you'll see doing shit which overall always +^%*'s up the power showings
Ex. Base Goku vs Hit/ SS Goku vs Hit....Base Goku vs Frieza...Because he's the only exception for common sense showings it throws a wrench in the whole thing When Vegeta fights Frost & goes SS to beat him; Why? Why when Vegeta can do the same in Base its inconsistent. Also Vegeta vs Cabba, they appear to be equals & yet worst Vegeta comments on them almost being equals also.....Inconsistent BS, because Canba can't go SS, SS2 or Use God Ki to go SSB; So how is his Base almost equal to Vegeta's...Inconsistent BS...Base Goku fights Hit, then SS Goku fights Hit...These all are bad showings because they aren't consistent in establishing an hierarchy of power. Then we get a super poor explanation of Vegeta being @ 1/10 power. Yet Goku's SSG (RED) appears to be stronger than this ridiculous development of Vegeta being @ 1/10 power.
So SSBG should be a thing but it's not, it's a inconsistent power showing that DBS/Z universe doesn't clean up properly...So vague folklore pops up outta every corner of fans imagination
So as to
How is it that they are so strong in their base form? (rlly Kckk, did you just ask how a characters base form got stronger in a Shounen manga)
They all get stronger as the series progress...After BOG Movie; Goku lost SSG (RED) but still fought Beerus, they explained he kept some of that Strentgh...Then a whole new movie l8er we seen he's been training & can go SSB, Super Sayain form with God Ki....Of course their base form got stronger. that's never changed in DB
when a character is using Hardening's Haki his arm is turned black;
Observation Haki it'll be illustrated as it has been shown previously or some type of context & dailougue will be fit in to explain that a characters current feats are due to Observation Haki.
Touching logia/negating DF powers like observation Haki, it's already been put into context & dialogue that this is in effect.....
When DB wants to show us God Ki we get SSB, or a Charcter who is a God & through context we'll get to know his Ki is different.
We've never received a context that Goku & Vegeta have fought in their base form using God Ki besides during their training...But like I get it..it should be a thing but it's not & the term SSBG doesn't make sense because it's not a real thing or form