Here is why Universes is a "safe" assumption. Suppose it actually is consistent. Then it cannot possibly prove any arithmetical statement that contradicts an arithmetical theorem of PA or ZFC. This is because it proves that PA and ZFC have "internally standard" interpretations, and so everything that they prove about the naturals is true of the "standard" model (i.e. within the theory ZFC+Universes), and thus agrees with everything "true" (true according to ZFC+Universes).
If we further assume that ZFC+Universes has an actually standard model, then this means that all its arithmetical theorems are actually true. But this kind of begs the question, I think. We would like to know about some kind of coherency between various theories at a syntactical level, that they don't prove contradictory arithmetical statements.
The idea, I believe, is that if we can organize them linearly in a "standard interpretation hierarchy," then we are fine as long as we believe in the consistency of the strongest theory under consideration. To be more precise, we look at theories $T$ which have a "natural numbers object" $\mathbb N^T$, which should at least satisfy PA, and should probably be proven by $T$ to satisfy second-order PA. If $S$ is another such theory, and $T$ proves that $S$ has a model $\frak A$ such that $\mathbb N^{\frak A} = \mathbb N^T$, then $T$ and $S$ cannot disagree about what their respective natural numbers object satisfies.
This situation applies to large cardinal axioms more generally.