Carbon steel used for heat excahngers is very susceptable to standby corrosion and pitting when new or following use. When excahangers or coolers are fabricated in a shop they are usually hydrotested with water of whatever quality is available then drained. Corrosion will begin at this time. If you have your own people witness the hydro, perhaps you can have them get the fabricator to flush and hold an inhibitor in the equipment for a period of time, usually several hours, then drain it. This may be an additional cost to the project but well worth it.
Your water treatment supplier is correct in recommending you to flush and hold the equipment with an inhibitor, typically 3X the normal dose during operation before putting it into service. In some cases, particularly high pressure BFW exchangers, acid cleaning is needed, to prevent minute amounts of iron from reaching the boilers, which is usually followed by a neutralizing and passivating step.
In the case of new carbon steel boilers, an alkaline boil out is performed. This removes oils & grease from rolling tubes in place and to promote a dense protective oxide film.
All of the above are for short term periods prior to putting the equipment into service. If you plan to keep the equipment in standby for weeks or months, then you need to devise a long term standby program such as nitrogen capping, a suitable wet method, cryogenic or dehumidified air. Keep in mind environmental conditions such as rain, humidtiy and deposit composition for instance when you have the fire side of a boiler in standby. All will need frequent monitoring and inspection.