Yes, using K might be safer than using Khex or Kbase64, for a down-to-earth reason distinct from the valid theoretical reason pointed in Henrick Hellström's answer.
RFC 2104 says:
The authentication key K can be of any length up to B, the block length of the hash function.
Applications that use keys longer than B bytes will first hash the key using H and then use the resultant L byte string as the actual key to HMAC.
If K is B bytes (or somewhat less), it will be used as the effective key to HMAC, but Khex or Kbase64 will first be hashed to size L. Knowledge of H(Khex) or H(Kbase64), which is L bytes, allows forgery! Whereas, arguably, when K is used directly, the actual entropy entering HMAC is equivalent to K or 2L bytes, whichever is smaller (notice that K XOR opad and K XOR ipad are separately compressed to L bytes during the first round of each distinct invocation of H).
Update: I initially got B and L mixed up in the first sentence of the above paragraph; that's fixed, thanks to Henrick Hellström's comment. And I missed the reduction of entropy to at most 2L bytes; that fixed, thanks to CodesInChaos's comment.
When H is MD5, B=64 bytes, L=16 bytes. When K is random and 64-byte, that's 512 bits of effective entropy for K, of which arguably 256 bits are used, versus 128 bits when using Khex or Kbase64.
While one 128-bit key seems safe for one or two decades even accounting for foreseeable technology improvements (depending on the confidence level required), there are plausible applications of HMAC-MD5 where this matters right now: should the adversary be able to obtain the HMAC-MD5 of the same message hashed using $n=2^{30}$ random keys, a brute force attack using feasible amount of memory is expected to find one of the key after only $2^{130}/n=2^{100}$ MD5 rounds, and that's uncomfortably close to attackable with a sizable chance of success.