Generally such entry is only permissible in an emergency. SSMA 2015 [s122(3)] or, by Tribunal Order.

[s122(3)] states: In an emergency, the owners corporation may enter any part of the parcel for those purposes at any time.

Without knowing more details, the situation that you described does not appear to fall within the definition of an “emergency”. There is no definition under the Act of an “emergency” therefore the ordinary dictionary meaning would probably apply. 

“emergency” – a serious, unexpected, and often dangerous situation requiring immediate action.

Whilst the asbestos situation may arguably be dangerous the unauthorized entry to your Lot for the purposes of taking photos for a future AGM is hardly going to provide an immediate remedy to the dangerous situation. It would probably not be wise for the person who authorized the entry to your Lot in this manner to rely on [s122(3)] as a defense. 

The balcony might be common property. 

Also, if loose asbestos were a possibility, I would not want some amateur risking disturbing it. I would want an expert taking appropriate precautions to look in my roof. 

What are the reasons that the EC are using for not obtaining an assessment? Is it the cost of the assessment? Is it fear of the repercussions if loose fill asbestos was actually found? Or is it something else? Would the insulation have been installed at the time that the building was built or would it have been installed by a previous owner? Would all Lots have the same potential problem?

https://www.fairtrading.nsw.gov.au/ftw/Tenants_and_home_owners/Loose_fill_asbestos_insulation/Living_in_strata.page?

Apparently there was a program of free assessments available to strata schemes during 2016 but the deadline has now passed. It was offered by the Office of Fair Trade and the assessments were conducted by Licensed Asbestos Assessors.

From the OFT site:

What if my property is within a strata scheme?  

Strata schemes that did not register for free testing prior to the 2016 registration deadline and are concerned that the property may contain LFAI should arrange for sample testing at their own expense.

To have been eligible for free testing, strata schemes will have lodged their intent to register with Fair Trading prior to the 2016 deadline and followed up by sending the approved special resolution to Fair Trading before 31 March 2017. 

Lot owners should be aware of the implications of a strata scheme being found to contain loose-fill asbestos insulation. Visit the New Laws page on the NSW Fair Trading website for more information. Lot owners and tenants of affected properties are potentially eligible for a range of assistance measures under the Government’s Voluntary Purchase and Demolition Program.

If loose-fill asbestos insulation is found in the strata scheme, individual lot owners will be contacted to arrange for the next phases of the Program. You can read more on the valuation and acquisition processes page on the NSW Fair Trading website.

If the strata scheme did not lodge their intent to register prior to the registration deadline and there is concern that the property contains loose-fill asbestos insulation, the scheme arrange for an LAA to conduct a sample test at their own expense

Did your scheme participate in this scheme? If it didn’t then the OC will need to pay for any assessments by a Licensed Asbestos Assessor.

https://www.fairtrading.nsw.gov.au/ftw/Tenants_and_home_owners/Loose_fill_asbestos_insulation.page

The Home Building Act 1989  states that all properties with loose fill asbestos must be able to be identified on a publicly available Loose-Fill Asbestos Insulation Register.

If loose fill asbestos is found then Disclosure needs to be made available to any potential buyers, and any occupant of the property including tenants, and any people who work on the property.

The affected premises will also be ‘tagged’, which means a government-approved label is required to be placed at the electrical meter box.

If you are not getting a satisfactory response from the SC about an asbestos assessment then you could by pass them and go straight to the OC.

You could contact an asbestos assessor to obtain a written quote for this service, then submit a Motion for inclusion in the next General Meeting stating:

That the Owner’s Corporation, Strata Plan xxxxxxxxxxx hereby resolves to authorise the approval of the obtaining of an asbestos assessment report by xxxxxxxx ,a licensed asbestos assessor, at a cost of xxxxxxxxxxx to determine whether the common property ceilings contain loose fill asbestos insulation and that the Owners permit access by the assessor to those areas of the common property for the purposes of taking samples of the insulation material from the ceiling space for testing, for a technical analysis of the samples to be undertaken and for a report on the testing to be produced.

Fill in the spaces with the info when you obtain it. Include the quote. Have the OC vote on it. 

You can find a list of assessors in your area via this link:

https://www.safework.nsw.gov.au/information-searches/asbestos-and-demolition-licence-holders