SDIO slave busy state
SD Specifications Part 1: Physical Layer Simplified Specification is relatively clear on this subject.


  The block write operation uses a simple busy signaling of the write operation duration on the DAT0 data line (see Figure 3-6) regardless of the number of data lines used for transferring the data.


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  The CRC status response and Busy indication will be sent by the card to the host on DAT0 only (DAT1-DAT3 during that period are don't care).


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  The card may provide buffering for block write. This means that the next block can be sent to the card while the previous is being programmed. If all write buffers are full, and as long as the card is in Programming State (see SD Memory Card state diagram Figure 4-13 ), the DAT0 line will be kept low (BUSY).


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  When reselecting the card, it will reactivate busy indication by pulling DAT to low if programming is still in progress and the write buffer is unavailable.


Thus in general you are correct; DAT0 (or MISO for SPI) will be pulled low in specific circumstances - for example while card is writing data to the card (only after you wrote data block with its CRC into the card), while it reads data (after you issued proper read command and card responded with successful command reception). And you can deselect the card while it is busy - to perform operations on other cards in the stack, and then reselect it to see if it is still busy or you may continue working on it.