From what I herd the SDHC cards should work on almost all standard
Micro-SD compatible devices. Is that incorrect?
That is incorrect.
Wikipedia said:
A new SD format, SDHC (Secure Digital High Capacity), allows capacities in excess of 2GB (4GB to 32GB). SDHC uses the same form factor as SD, but the SD 2.0 standard in SDHC uses a different memory addressing method (sector addressing vs byte addressing). 4GB SDHC cards can only work with SDHC compatible host devices.Wikipedia
  * Devices that do not specifically support SD2.0/SDHC do not recognize SDHC memory cards.
  * Some manufacturers have produced 4GB SD cards that do not conform to the SD2.0/SDHC spec and are incompatible with existing SD devices, and are also incompatible with SDHC devices. Prior versions of the SD spec do not allow for 4GB cards.