Someone told me that Peach's float allows her to quickly perform full-strength aerials close to the ground in a short hop-like situation. Is this actually the case?

To clarify, the short hop multiplier does not directly change knockback. Instead, it lowers the damage of short hop aerials by 15% (to 85%). The knockback is only reduced because it's calculated after the damage, and opponents with less damage get knockbacked less. This is only a small reduction in knockback.

Back to your question, yes, Peach's (and Daisy's) float negates this multiplier. This makes Peach's (and Daisy's) aerials relatively more damaging and with greater shieldstun. They can be performed anywhere in the air, including close to the ground as per this demonstrative video. This same video later highlights the potency of these aerials' increased damage and shieldstun through combos that rack up damage quickly and imply strong shield pressure.

Yes. If Peach (or Daisy) Float Cancel, they’re not affected by the Short Hop Modifier

@MBorg's answer is right on the money. But I'd like to supplement it with some visuals:

Like they explain, for all characters, any aerial performed out of a shorthop will have a .85x damage modifier attached to it. For example, with an un-staled Ganon down-air performed from both a short and full hop:

^{(for those of you at home, 23.9 x .85 = 20.315 = ~20.3)}

But with Peach, as MBorg has noted, things are a little different...

Here's an un-staled Peach back-air from a short hop, full hop and then a float cancel (please forgive my terribad video editing):

Notice how--while the short hop deals only 12.8%--both the full hop and float cancel clock in at the same amount of damage: 15.1%!

This is something I've seen many players in the community clamoring about nerfing. It's a disadvantage everyone has except Peach! While less damage means less knockback (given the way knockback operates) which means potentially more combos, Peach already has some devastating 0-80% combos with her float cancels as they are!

With Balance Patch 3.1.0 dropping any day now, we'll see if this gets touched...