Why MUST an index be sparse to be used in a DocumentDB query with an $exists clause?

Given a DocumentDB collection called test, with 200 documents of the following shape (i.e. containing a simple key/value pair):

{ "num" : 1 }

and an index on the key num:

{ v: 4, key: { num: 1 }, name: 'num-idx', ns: 'db.test2' }

the index is not used for the following query:

db.test.find({'num': {$exists: true}})
...
winningPlan: { stage: 'COLLSCAN' }

This is consistent with the AWS documentation which states:

Amazon DocumentDB does not currently support the ability to use indexes with the $ne, $nin, $nor, $not, $exists, $distinct, and $elemMatch operators. As a result, utilizing these operators will result in collection scans

However when I recreate the index, specifying it is sparse:

{  v: 4, key: { num: 1 }, name: 'num-idx', ns: 'db.test2', sparse: true }

then the index IS used:

db.test.find({'num': {$exists: true}})
...
winningPlan: { stage: 'IXSCAN', indexName: 'num-idx', direction: 'forward' } }

According to the MongoDB documentation, making an index sparse has the following implications:

• documents missing the indexed keys will not be present in the index
• this makes the index smaller in memory
• you cannot use it for queries containing { $exists: false }

There is no mention of the sparsity of an index being a requirement in order for it to be used in the case of { $exists: true } queries.

The closest to an answer I can find is https://docs.aws.amazon.com/documentdb/latest/developerguide/functional-differences.html#functional-differences.sparse-index piece of AWS documentation which states:

To use a sparse index that you have created in a query, you must use the $exists clause on the fields that cover the index. If you omit $exists, Amazon DocumentDB does not use the sparse index

However, this clashes with the previous documentation quote.

Behaviour for MongoDB (db.test.find({'num': {$exists: <VALUE>}})):

Head	exists:true	exists:false
sparse index	IDX	COLLSCAN
non sparse index	IDX	IDX

Behaviour for DocumentDB (db.test.find({'num': {$exists: <VALUE>}})):

Head	exists:true	exists:false
sparse index	IDX	COLLSCAN
non sparse index	COLLSCAN	COLLSCAN

Is this an unintended loophole?

Can I rely on this behaviour to guarantee that a query containing an { $exists: true } clause is able to use an index if it is sparse?