It all comes down to "what do you mean by 'private network'" doesn't it?
If you operate an IP network which is air-gapped from all other IP networks, which IP address you use is irrelevant. If that network interconnects with (only) a provider/customer using RFC 1918 space, you either have to coordinate with them, NAT, or use non-RFC 1918 space.
If you run a network which should only communicate with others through a proxy/firewall/NAT device, how much does it matter what's on the inside?
Of course, the risk of using IP addresses which are not uniquely assigned to you is that there will be an overlap somewhere. Whether the risk is greater inside or outside of RFC 1918, I leave for others to puzzle out (although it should be noted that organizational M&A activity makes hash of the best-laid IP address schema).
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