Contrary to Sister Aloysius' teachings, some nonsensical statements can be unimpeachably grammatical.
Your dangling modifier can be ludicrous, yet your statement can be perfectly grammatical, as this Tweet demonstrates:
We develop tests for flu and other diseases that help patients.
You can ignore an absolute quality, yet your statement can be perfectly grammatical, as this web ad headline demonstrates:
Transparency you will see.
You can flout a determiner, yet your statement can be perfectly grammatical, as this newspaper headline demonstrates:
One-armed man applauds the kindness of strangers.
Your decision to recast statements like the three above is a matter of judgement, not grammar.
By letting them stand, you risk slowing readers, confusing them, or inviting them to think you're a dope.
But you don't deserve Sister's wrath.
NOTE: The examples you have just seen are true. The names have been withheld to protect the innocent. For more examples, read the final chapter of Steven Pinker's The Sense of Style.
