tl;dr– The terms "because" and "on the grounds" mean different things. "Because" is for causation, "on the grounds" is for justification. Ideally causation and justification align in simple legal scenarios, allowing the shorter "because" to be favored. Use of "on the grounds" might suggest that the scenario wasn't simple enough for "because" to have been appropriate.
"Because" for causation; "on the grounds" for justification.
To better define the terms:
"Because" describes why something is. Literally, constructed from
cause, i.e. the cause of something's being. (Also
"On the grounds" describes the underlying platform for an argument. Literally, an argument rests on the logical-underpinning (grounds) of [whatever].
For example, say Alice purchased something online, but the product wasn't as-described. Then:
These weren't interchangeable. For example, say Alice got a product that was much better than described: even though she'd seem to have the same basis for getting her money back, presumably she wouldn't want to. On the flip-side, Alice might want her money back even if the product was as-described if she later changed her mind about the purchase.
"Because" sometimes approximates "on the grounds".
Usually events could happen for a wide variety of reasons. For example, part of why Alice was late to school was that the school was built; if it wasn't built, then Alice couldn't have been late to it. Still, we wouldn't generally say that Alice was late because the school was built.
So, say that Alice got a coupon for a free gift at a store. Usually:
That said, Alice probably wouldn't normally try to not-pay for an item; so, we can say that part of why Alice didn't pay was because of the coupon. This is like the above example of Alice being late to school because the school was built: it's technically true, if a bit off-target.
Point being that if someone has grounds for an argument to do something, then having those grounds may be part of why they'd do it, such that we might say that "because" can sometimes be a somewhat off-target substitute for "on the grounds".
How these terms differ in judicial settings.
Often folks hope that legal-reasoning would align causation with justification, making the terms "because" and "on the grounds" interchangeable.
For example, say there's a law:
If Alice buys an item, she must pay tax equal to 10% of its price.
Alice would pay 10% sales-tax because she wants to comply with the law, which says that she must do so.
Alice would pay 10% sales-tax on the grounds that the law says she must do so.
And if we assume that people generally want to comply with the law in a simple legal-setting, then presumably we can simplify the above examples which would then be basically the same thing.
However, say that there's a law:
If Alice and Bob conflict, then Charlie can pick who wins.
If Charlie picks Alice or Bob as the winner, then Charlie could do so on the grounds of that law – though since the law seems indifferent to Alice vs. Bob, presumably we couldn't say that Charlie picked Alice or Bob over the other because of the law.
In simple cases in which either term could work, writers might prefer "because" for brevity. However, in more complex cases in which causation and justification aren't so interchangeable, writers might have to specify the more verbose "on the grounds".
"Because" and "on the grounds" mean two different things; they're not generally interchangeable.
Legal settings can be a special exception, because ideally causes of legal action are well-aligned with legal justification. When such alignment exists and either term works, presumably "because" would be favored since it's shorter/simpler, while use of the more verbose "on the grounds" may suggest that things aren't quite as straightforward.
However, more precise speakers might avoid conflating "because" and "on the grounds", so it'd probably be good to avoid broadly assuming that "on the grounds" generally implies skepticism.