Not the case if you maintain the same notional exposure. There isn't any inherent risk in a naked put that isn't also in the covered call.
The risk that you inadvertently described is over-leveraging. The circumstance in which a naked put seller would get a margin call while the covered call writer would be fine is one in which the naked put seller increased his exposure. This leads us to a good rule of thumb for any beginning options trader.
Try to maintain the same notional exposure that you could tolerate if you were utilizing the inferior equivalent. In this case that is the covered call. That is, if you would be comfortable buying 1000 shares and selling 10 calls, then only sell 10 puts at the equivalent strike. Use the free margin wisely and fully utilize the advantages of the naked put.
edit:: Just so that I don't have to explain myself later. If the above covered call tied up $50K, it is likely that the naked put would only tie up <$25K. If the move against you is large, sure the covered call guy will be able to simply sit it out. The naked put guy has an extra $25K in his account that wasn't originally tied up in the trade. If it is sitting in cash, then he will not get a margin call. A good broker will allow him to invest the spare cash in fixed income investments to increase his return while at the same time using those securities as backing for the naked put in case of a margin call. Hence, the margin call is not an issue if notional exposure is maintained.