I'm here to support stjvilla's comment.  Good points made.

I would not take it so personally...."....refuses to rent because they don't like you". This is a case  of someone who wants to rent while she is afraid to rent.....and employs an agent with a heavy hand in "screening".  It isn't personal....it's business.  You've done nothing to offend or appear "suspect" to the agent.  It's a weird arrangement, though, from the get-go, in my opinion.

Personally, I would not try to work out anything with this agent.  I wouldn't even try to work directly with that owner.  Under those rental circumstances...after what the agent revealed about the owner's insecurity renting the place, I'd perfer to stay away from it...I would  not want to feel "responsible" for anything.   One never knows if anything should go "missing", "misplaced"  or just damaged.... from among all her personal belongings she has there...what you could be suspected of, charged a fee for...and falsly accused of...who knows?

It's actually an 'unspoken'  fact that most owners generally do screen inquirers a little so we know who we are giving the keys to our house to.....even for a short stay. We just expect essential information.  But, this one seemed unprofessional and a bit of an interrogation. {Unless you speak Italian....the agent was speaking English to you.  ?...and perhaps his command of English was awkward ...so his tone could sound wrong when trying to make a point in a foreign language.  Just a consideration from someone who lived and worked in different countries and had to learn languages...struggled to express myself well.  Just a side thought, I had}.

Regardless, this all sounded "over the top".  The owner seems to have criteria to "qualify" a renter...or it's an agent acting on his own to protect his client...even if it sounds extreme....there's plenty of crime in Milan.

You dealt with that agent  once before, so it seems it's not so unusual.  But, the owner should not put all her personal belongings in her home open to risk, regardless.   Foolish. That's a different discussion.

Does this warrent an online compliant...to harm the woman?   I don't know....I'm not so sure that I would want to do that, personally. They have their modis operandi ...maybe it's standard practice  in Milan...maybe not....and she has her criteria that "qualifies" guests.

But, owners do have the prerogative to select who they will rent to...who they feel secure giving the keys to. I do not rent to anyone and everyone who inquires, for example...if it's not a good match....I need basic information about who wants my keys. That's all.   I do not interrogate, but I do like to know what brings someone to my location ...to rent my home?  Vacation?  Business?  Family gathering?  That comes out "in the booking process"....because there are rental terms and conditions to be considered by both parties.   If you're  a single guy on business in my area, I'd welcome you....as long as you sign my rental agreement which states that you accept my terms.....I'd warmly welcome you.

I think that this  owner lost a good guest opportunity - you!  It's her loss.

Personally, I would just  move on to find another place...try a different agent...or use HA and VRBO to work directly with the owner.

You will find a better rental in Milan with more reasonable reservation procedure and rental terms.  You are correct....this trade depends upon TRUST between both parties.